Static Deformation of Fluid-Saturated Rocks
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 Willi...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Technical Report |
| Published: |
Massachusetts Institute of Technology. Earth Resources Laboratory
2012
|
| Online Access: | http://hdl.handle.net/1721.1/75060 |
| _version_ | 1826202677180104704 |
|---|---|
| author | Coyner, Karl |
| author2 | Massachusetts Institute of Technology. Earth Resources Laboratory |
| author_facet | Massachusetts Institute of Technology. Earth Resources Laboratory Coyner, Karl |
| author_sort | Coyner, Karl |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T12:13:52Z |
| format | Technical Report |
| id | mit-1721.1/75060 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T12:13:52Z |
| publishDate | 2012 |
| publisher | Massachusetts Institute of Technology. Earth Resources Laboratory |
| record_format | dspace |
| spelling | mit-1721.1/750602019-04-12T20:28:05Z Static Deformation of Fluid-Saturated Rocks Coyner, Karl Massachusetts Institute of Technology. Earth Resources Laboratory Coyner, Karl 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. Massachusetts Institute of Technology. Full Waveform Acoustic Logging Consortium Geophysical Services Inc. (Grant P06077-W63550) 2012-11-27T20:31:57Z 2012-11-27T20:31:57Z 1984 Technical Report http://hdl.handle.net/1721.1/75060 Earth Resources Laboratory Industry Consortia Annual Report;1984-12 application/pdf Massachusetts Institute of Technology. Earth Resources Laboratory |
| spellingShingle | Coyner, Karl Static Deformation of Fluid-Saturated Rocks |
| title | Static Deformation of Fluid-Saturated Rocks |
| title_full | Static Deformation of Fluid-Saturated Rocks |
| title_fullStr | Static Deformation of Fluid-Saturated Rocks |
| title_full_unstemmed | Static Deformation of Fluid-Saturated Rocks |
| title_short | Static Deformation of Fluid-Saturated Rocks |
| title_sort | static deformation of fluid saturated rocks |
| url | http://hdl.handle.net/1721.1/75060 |
| work_keys_str_mv | AT coynerkarl staticdeformationoffluidsaturatedrocks |