Abstract
Measurements of complex electrical conductivity as a function of frequency is an extremely sensitive probe for changes in pore and crack volume, crack connectivity, and crack surface topography. Such measurements have been made as a function of pore fluid chemistry, hydrostatic codning pressure, as well as uniaxial and tnaxial deformation. This paper develops a method for using such experimental conductivity data to model the mechanical properties of saturated rocks undergoing triaxial deformation. It does so by defming a new direction sensitive crack damage parameter denved from the electrical data on four samples of Darley Dale sandstone. More specifically this paper will: 1) review the theoretical concepts necessary to understand the modelling procedure (crack density parameter and effective elastic properties of cracked solids), 2) derive a new crack damage parameter from electrical conductivity data, 3) use the electrical data to model the mechanical stress-strain behavior of porous rocks, and 4) compare the modelled results with the stress-strain behavior measured during the deformation. The resultant synthetic stress-strain curves show good agreement with the experimentally derived stress-strain curves, and the estimated values of model parameters also compare well with their experimental counterparts. This modelling is an improvement on similar curves produced using isotropic crack damage parameters, such as those denved from acoustic emission data. The improvement is likely to be due to the directional sensitivity of the electrical conductivity measurement, and its ability to discriminate between the formation of isolated cracks, and those cracks that contribute to the interconnected crack space, i.e., those cracks upon which both the transport properties of the rock such as electrical conductivity, and the mechanical properties depend most critically during triaxial deformation.
Highlights
Measurements of complex electrical conductivity as a function of frequency is an extremely sensitive probe for changes in pore and crack volume, crack connectivity, and crack surface topography
Los parámetros de densidad de grietas basados en los cambios en las velocidades de las ondas elásticas son los más comunes en la literatura geofísica (O'Connell y Budiansky, 1974, Anderson et al, 1974, Soga et al, 1978, Sayers, 1988, Yukutake, 1989 y Ayling et al, 1995)
El resultado de aplicar la ecuación (42) a los datos de conductividad eléctrica a 1 kHz se muestra en la figura 9, que es un gráfico de la evolución de la porosidad eléctrica en función de la deformación y del esfuerzo para las muestras TRYl, TRY2 Y TRY4
Summary
La medida de la conductividad eléctrica compleja en función de la frecuencia en rocas durante los experimentos de deformación triaxial es una técnica muy sensible para determinar los cambios en el volumen de poros y grietas y en la conectividad y la topografía superficial de las grietas. Los datos experimentales de conductividad eléctrica registran la evolución deformacional de la roca desde la fase inicial en la que se pierde volumen por compactación, seguida de la fase de dilatación debido a la formación de nuevas grietas y al crecimiento y coalescencia de las preexistentes, hasta la rotura macroscópica de la muestra. Se han usado estos datos de conductividad eléctrica tomados en cuatro experimentos sobre muestras de arenisca Darley Dale para calcular un parámetro de densidad de grietas sensible a la dirección axial de las muestras y, a partir de él, se ha calculado el módulo de Young efectivo usando diversos modelos de sólidos fracturados (modelo sin interacción, modelo autoconsistente y modelo diferencial). Palabras clave: Deformación triaxial, Rocas, Conductividad eléctrica, Curvas esfuerzo-deformación, Parámetro de densidad de grietas, Modelos de sólidos fracturados
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