HIREARCHICAL MODEL OF THE STRUCTURE OF A POROUS, SATURATED, DEFORMABLE MEDIUM

Abstract

The paper discusses a model of a granular porous medium whose microstructure is formed by rigid grains separated by compliant partings. The grains form conglomerates of various scales, with a definite size hierarchy. Numerous recent data in the geophysical literature show that the crust consists of blocks of various sizes. This hierarchical structure obeys a definite pattern, namely, that the ratio of the large dimension of a cell to the adjoining smaller dimension is constant and close to 3. Some similitude principle, according to which the structure of the system is approximately the same at different size levels, is operative. This principle is based on indirect (primarily seismologic) data and therefore still has not been clearly formulated for a rheologic system in which no breakdown or failure processes occur. The present paper reduces to specifics the concepts of a hierarchical block structure by using the principle of similitude, understood as a similitude of the geometric scales of structures in the case in which the rheological properties of the medium at different size levels are identical. The governing equations are derived for consolidation and percolation for an ordered multiscale (multisize) structure and it is demonstrated that the governing equations for any relationship between scales can be derived analogously in the context of this model.