An examination of scale-dependent electrical resistivity measurements in Oracle granite.

Persistent Link:
http://hdl.handle.net/10150/184887
Title:
An examination of scale-dependent electrical resistivity measurements in Oracle granite.
Author:
Jones, Jay Walter, IV.
Issue Date:
1989
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Geotechnical characterization of crystalline rock is often dependent upon the influence of the rock's fracture system. To test ensemble fracture behavior in situ, a series of cross-hole and single-hole electrical conductivity measurements were made within saturated Oracle granite. The tests were conducted with a point source and a point reference electrode and employed electrode separations ranging from 8 inches to over 100 feet. A volume of rock approximately 50 x 50 x 150 feet was tested (as bounded by the vertical test borings). Analysis of the data in terms of an equivalent homogeneous material showed that the effective electrical conductivity increased with electrode separation. The cross-hole data indicate that the rock can be treated as a non-homogeneous, isotropic material. Further, the spatial variation of measured conductivities along a line can be fit to a fractal model (fractional Brownian motion), implying that the scale-dependence is a result of a fractal process supported by the fracture system. Scale-dependence exists at the upper scale limit of the measurements, hence a classical representative elemental volume was not attained. Two directions were taken to understand the scale-dependence. The rock mass is treated in terms of a disordered material, a continuum with spatially varying conductivity. First, a percolation-based model of a disordered material was examined that relates the conductivity pathways within the rock to the backbone of a critical percolation cluster. Using the field data, a fractal dimension of 2.40 was derived for the dimensionality of the subvolume within the rock that supports current flow. The second approach considers an analytic solution for a non-homogeneous, isotropic material known as the alpha center model (Stefanescu, 1950). This model, an analytic solution for a continuously varying conductivity in three dimensions, is a non-linear transform to Laplace's equation. It is employed over a regular grid of support points as an alternative to spatially discretized (piece-wise continuous) numerical methods. The model is shown to be capable of approximating the scale-dependent behavior of the field tests. Scaling arises as a natural consequence of the disordered electrical structure caused by the fracture system.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Rock mechanics; Crystalline rocks -- Electric properties -- Arizona -- Oracle Region; Granite -- Arizona -- Oracle Region.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Mining and Geological Engineering; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Glass, Charles E.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleAn examination of scale-dependent electrical resistivity measurements in Oracle granite.en_US
dc.creatorJones, Jay Walter, IV.en_US
dc.contributor.authorJones, Jay Walter, IV.en_US
dc.date.issued1989en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractGeotechnical characterization of crystalline rock is often dependent upon the influence of the rock's fracture system. To test ensemble fracture behavior in situ, a series of cross-hole and single-hole electrical conductivity measurements were made within saturated Oracle granite. The tests were conducted with a point source and a point reference electrode and employed electrode separations ranging from 8 inches to over 100 feet. A volume of rock approximately 50 x 50 x 150 feet was tested (as bounded by the vertical test borings). Analysis of the data in terms of an equivalent homogeneous material showed that the effective electrical conductivity increased with electrode separation. The cross-hole data indicate that the rock can be treated as a non-homogeneous, isotropic material. Further, the spatial variation of measured conductivities along a line can be fit to a fractal model (fractional Brownian motion), implying that the scale-dependence is a result of a fractal process supported by the fracture system. Scale-dependence exists at the upper scale limit of the measurements, hence a classical representative elemental volume was not attained. Two directions were taken to understand the scale-dependence. The rock mass is treated in terms of a disordered material, a continuum with spatially varying conductivity. First, a percolation-based model of a disordered material was examined that relates the conductivity pathways within the rock to the backbone of a critical percolation cluster. Using the field data, a fractal dimension of 2.40 was derived for the dimensionality of the subvolume within the rock that supports current flow. The second approach considers an analytic solution for a non-homogeneous, isotropic material known as the alpha center model (Stefanescu, 1950). This model, an analytic solution for a continuously varying conductivity in three dimensions, is a non-linear transform to Laplace's equation. It is employed over a regular grid of support points as an alternative to spatially discretized (piece-wise continuous) numerical methods. The model is shown to be capable of approximating the scale-dependent behavior of the field tests. Scaling arises as a natural consequence of the disordered electrical structure caused by the fracture system.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectRock mechanicsen_US
dc.subjectCrystalline rocks -- Electric properties -- Arizona -- Oracle Regionen_US
dc.subjectGranite -- Arizona -- Oracle Region.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineMining and Geological Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorGlass, Charles E.en_US
dc.contributor.committeememberSternberg, Ben K.en_US
dc.contributor.committeememberFarmer, Ian W.en_US
dc.contributor.committeememberNeuman, Shlomo P.en_US
dc.contributor.committeememberBentley, Harold W.en_US
dc.identifier.proquest9013148en_US
dc.identifier.oclc703435347en_US
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