Pendulum waves and basics of «geomechanical thermodynamics»

Abstract

It is shown that modern achievements in the field of experimental and theoretical researches and developments of innovative measuring systems for monitoring of non-linear dynamic and kinematic characteristics allow to formulate basics of new academic discipline, designated as “geomechanical thermodynamics”. The following circumstances can be considered as the most important prerequisites for development of this new discipline.

(1) Practical completeness of the classical thermodynamics, based on kinetic gas theory and molecular movements in solid bodies; (2) Creation of “formular construction tool” for the description of dynamic and kinematic characteristics of pendulum waves and energy conditions of their occurrence and propagation from dynamic sources, located in multi-phased stressed rock mass and geomaterials with block-hierarchical structure; (3) Principal opportunity to establish formal relations between substantial energy carriers of “packages” of non-linear pendulum waves (geoblocks of certain hierarchical levels according to their diameters) and “molecules”: their movement, velocity and acceleration of the “molecules” ↔ “geoblock”; “force interactions between molecules” ↔ “non-linear elastic interaction between geoblocks”, etc.

The term of “geomechanical temperature” is introduced and its analytical expression, which is proportional to kinetic energy of movement of geoblocks with defined volume for their hierarchical subsequence at “confined” conditions of the stressed rock mass, is shown. The similar aspects are discussed, when emission acoustic-electromagnetic fields are fixed using corresponding coefficients of mechanical-electrical and mechanical-acoustic transformations. In order to quantitively describe the evolution of energy state of local zones of stress-strain concentration and surroundings of their non-linear influence from catastrophic events at the natural and mine-engineering systems (earthquakes, rock bursts, etc.), the terms of their geomechanical and thermodynamic stages are introduced and specified: $T_i\left(i\in 0,+,\pm ,-,\ast \right)$‒ with background states $\left(i\in 0,\ast \right)$ and three major stages $\left(i\in +,\pm ,-\right)$ outlined, where (+) is the concentration, (±, ‒) are the failure and relaxation and (∗) is the quasi-recovering up to “background” level after the occurred catastrophic event. Using certain examples, the existence of critical elastic energy content of local zones with “meta-stable state”, which is transforming to quasi-resonance process of failure and relaxation of “excessive” energy, is shown $\left(T_{\pm }\right)$.