| Summary: | The static strain response of porous solids to combinations of confining stress and pore pressure is explained both theoretically and experimentally. The theoretical analysis is a synopsis of linear elasticity principles for porous media taken mainly from Biot (1941), Gassmann (1951), Biot and Willis (1956), and Geertsma (1957). From this analysis the conclusion is made that the "effective stress" of Terzaghi (1923, 1925), which is the difference between hydrostatic confining stress and pore pressure for strain properties, has no theoretical or experimental significance for the static strain response of intact rocks. The Terzaghi effective stress cannot account for the intrinsic bulk strain of minerals, a component of strain response important in consolidated
sediments and rocks but not in muds and soils, for which the Terzaghi relation
was originally intended. Effective stress "laws" for static deformation proposed
by Nur and Byerlee (1971), Garg and Nur (1973), Robin (1973), and Carroll
(1979) are shown only to be reformulations of linear elasticity relations. The
effective stress so defined has no intrinsic physical meaning. Experimental bulk
strain measurements on a suite of rocks as a function of hydrostatic confining
stress and pore pressure are presented. Equilibrium strain at any combination
of confining stress and pore pressure is predicted on the basis of 1) the zero
pore pressure or drained jacketed stress-strain relation, and 2) the unjacketed
stress-strain relation. Unjacketed strain measurements with a confining pressure fluid are emphasized as a means of directly measuring the intrinsic modulus of aggregate minerals in rocks. A technique is outlined for experimentally obtaining pore volume or porosity as a function of confining stress from finely digitized unjacketed and jacketed strain data by a straightforward application of linear elasticity principles incrementalized over small data steps. An argument is made, based on the linear elasticity analysis for strain response, that the differential hydrostatic stress, or what is commonly called effective stress, predicts many physical properties exclusive of
bulk strain because of 1) the large intrinsic moduli of minerals, and 2)the
definition of a stress as a force per unit area is maintained during deformation
because of the small strains normally encountered in consolidated rocks and sediments.
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