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Title: Estimates and Rigorous Bounds on Pore-Fluid Enhanced Shear Modulus in Poroelastic Media with Hard and Soft Anisotropy

Abstract

A general analysis of poroelasticity for hexagonal, tetragonal, and cubic symmetry shows that four eigenvectors are pure shear modes with no coupling to the pore-fluid mechanics. The remaining two eigenvectors are linear combinations of pure compression and uniaxial shear, both of which are coupled to the fluid mechanics. The analysis proceeds by first reducing the problem to a 2 x 2 system. The poroelastic system including both anisotropy in the solid elastic frame (i.e., with ''hard anisotropy''), and also anisotropy of the poroelastic coefficients (''soft anisotropy'') is then studied in some detail. In the presence of anisotropy and spatial heterogeneity, mechanics of the pore fluid produces shear dependence on fluid bulk modulus in the overall poroelastic system. This effect is always present (though sometimes small in magnitude) in the systems studied, and can be comparatively large (up to a maximum increase of about 20 per cent) in some porous media--including porous glass and Schuler-Cotton Valley sandstone. General conclusions about poroelastic shear behavior are also related to some recently derived product formulas that determine overall shear response of these systems. Another method is also introduced based on rigorous Hashin-Shtrikman-style bounds for nonporous random polycrystals, followed by related self-consistent estimates of mineralmore » constants for polycrystals. Then, another self-consistent estimation method is formulated for the porous case, and used to estimate drained and undrained effective constants. These estimates are compared and contrasted with the results of the first method and a consistent picture of the overall behavior is found in three computed examples for polycrystals of grains having tetragonal symmetry.« less

Authors:
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
881888
Report Number(s):
UCRL-JRNL-209252
TRN: US200613%%176
DOE Contract Number:  
W-7405-ENG-48
Resource Type:
Journal Article
Journal Name:
International Journal of Damage Mechanics
Additional Journal Information:
Journal Volume: 15; Journal Issue: 2
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 58 GEOSCIENCES; 42 ENGINEERING; 54 ENVIRONMENTAL SCIENCES; ANISOTROPY; COMPRESSION; EIGENVECTORS; FLUID MECHANICS; GLASS; POLYCRYSTALS; SHEAR; SYMMETRY

Citation Formats

Berryman, J G. Estimates and Rigorous Bounds on Pore-Fluid Enhanced Shear Modulus in Poroelastic Media with Hard and Soft Anisotropy. United States: N. p., 2005. Web.
Berryman, J G. Estimates and Rigorous Bounds on Pore-Fluid Enhanced Shear Modulus in Poroelastic Media with Hard and Soft Anisotropy. United States.
Berryman, J G. Mon . "Estimates and Rigorous Bounds on Pore-Fluid Enhanced Shear Modulus in Poroelastic Media with Hard and Soft Anisotropy". United States. https://www.osti.gov/servlets/purl/881888.
@article{osti_881888,
title = {Estimates and Rigorous Bounds on Pore-Fluid Enhanced Shear Modulus in Poroelastic Media with Hard and Soft Anisotropy},
author = {Berryman, J G},
abstractNote = {A general analysis of poroelasticity for hexagonal, tetragonal, and cubic symmetry shows that four eigenvectors are pure shear modes with no coupling to the pore-fluid mechanics. The remaining two eigenvectors are linear combinations of pure compression and uniaxial shear, both of which are coupled to the fluid mechanics. The analysis proceeds by first reducing the problem to a 2 x 2 system. The poroelastic system including both anisotropy in the solid elastic frame (i.e., with ''hard anisotropy''), and also anisotropy of the poroelastic coefficients (''soft anisotropy'') is then studied in some detail. In the presence of anisotropy and spatial heterogeneity, mechanics of the pore fluid produces shear dependence on fluid bulk modulus in the overall poroelastic system. This effect is always present (though sometimes small in magnitude) in the systems studied, and can be comparatively large (up to a maximum increase of about 20 per cent) in some porous media--including porous glass and Schuler-Cotton Valley sandstone. General conclusions about poroelastic shear behavior are also related to some recently derived product formulas that determine overall shear response of these systems. Another method is also introduced based on rigorous Hashin-Shtrikman-style bounds for nonporous random polycrystals, followed by related self-consistent estimates of mineral constants for polycrystals. Then, another self-consistent estimation method is formulated for the porous case, and used to estimate drained and undrained effective constants. These estimates are compared and contrasted with the results of the first method and a consistent picture of the overall behavior is found in three computed examples for polycrystals of grains having tetragonal symmetry.},
doi = {},
url = {https://www.osti.gov/biblio/881888}, journal = {International Journal of Damage Mechanics},
number = 2,
volume = 15,
place = {United States},
year = {2005},
month = {1}
}