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Geometry, Mechanics and Transmissivity of Rock Fractures

by Lanaro, Flavio

Abstract (Summary)
This Thesis work investigates methods and tools for characterising, testing and modelling the behaviour of rock fractures. Using a 3D-laser-scanning technique, the topography of the surfaces and their position with respect to one another are measured. From the fracture topography, fracture roughness, angularity and aperture are quantified; the major features used for characterisation. The standard deviations for the asperity heights, surface slopes and aperture are determined. These statistical parameters usually increase/decrease according to power laws of the sampling size, and sometimes reach a sill beyond which they become constant. Also the number of contact spots with a certain area decreases according to a power-law function of the area. These power-law relations reveal the selfaffine fractal nature of roughness and aperture. Roughness is “persistent” while aperture varies between “persistent” and “anti-persistent”, probably depending on the degree of match of the fracture walls. The fractal models for roughness, aperture and contact area are used to develop a constitutive model, based on contact mechanics, for describing the fracture normal and shear deformability. The experimental testing results of normal deformability are simulated well by the model whereas fracture shear deformability is not as well modelled. The model predicts well fracture dilation but is too stiff compared to rock samples. A mathematical description of the aperture pattern during shearing is also formulated. The mean value and covariance of the aperture in shearing is calculated and verifies reported observations. The aperture map of samples is inserted in a numerical program for flow calculation. The “integral transform method” is used for solving the Reynolds’ equation; it transforms the fracture transmissivity pattern into a frequency-based function. This closely resembles the power laws that describe fractals. This function can be described directly from the fractal properties of the aperture, with noticeable economy of input data. The modelling also affirms that the density of the aperture data greatly affects the calculated flow.
Bibliographical Information:

Advisor:

School:Kungliga Tekniska högskolan

School Location:Sweden

Source Type:Doctoral Dissertation

Keywords:anisotropy; angularity; anti-persistence; aperture; channelling; closure; contact area; contact mechanics; cross-correlation; deformability; dilation; flow; fractals; fracture; joint; laboratory; modelling; normal loading; persistence; power spectra,

ISBN:91-7283-112-X

Date of Publication:01/01/2001

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