Instability of Cracked and Porous Media by Statics and Small Vibrations

摘要

The book introduces strain problems for high-contrast microinhomogeneous media featuring a very high (many orders of magnitude) difference in physical-mechanical properties between the matrix and the closing. These are oil, gas or water reservoir, coals and other fractured rocks. The classical continuum hypothesis is unsuitable for these media, since the classical continuum implies that close points should have close values of all physical properties (stresses, strains, temperatures etc). Rejecting the continuum hypothesis means either setting the boundary conditions at the whole internal pore surface or constructing a new continuum with initially specified collective geometrical properties of pores and fractures. The integral geometry describes these collective properties. This geometry substantially affects the physics of elementary strain process so that the equilibrium and motion equations differ radically from the classic ones. These equations describe, besides the regular effects, very slow waves, catastrophe dynamics and the intermediate states between statics and dynamics.