Accurate quantification of rock fracture aperture is important in investigating hydro-mechanical properties of rock fractures. Liquefied wood?s metal was used successfully to determine the spatial distribution of aperture with normal stress for natural single rock fractures. A modified 3-D box counting method is developed and applied to quantify the spatial variation of rock fracture aperture with normal stress. New functional relations are developed for the following list: (a) Aperture fractal dimension versus effective normal stress; (b) Aperture fractal dimension versus mean aperture; (c) Fluid flow rate per unit hydraulic gradient per unit width versus mean aperture; (d) Fluid flow rate per unit hydraulic gradient per unit width versus aperture fractal dimension. The aperture fractal dimension was found to be a better parameter than mean aperture to correlate to fluid flow rate of natural single rock fractures. A highly refined variogram technique is used to investigate possible existence of aperture anisotropy. It was observed that the scale dependent fractal parameter, Kv, plays a more prominent role than the fractal dimension, Da1d, on determining the anisotropy pattern of aperture data. A combined factor that represents both Da1d and Kv, Da1d × Kv, is suggested to capture the aperture anisotropy.


Rock fracture aperture, the void geometry distribution resulting from the separation or mismatch between the two surfaces of a fracture, plays an important role in the field of rock mechanics and fractured rock hydrogeology. Hydromechanical properties of a rock fracture depend very much on the aperture distribution of the fracture. Rock mass hydro-mechanical properties in turn depend very much on the hydro-mechanical properties of rock fractures. Therefore, characterization of aperture distribution is important to the study of hydro-mechanical properties of fractures in rock masses.

In engineering practice, some simple statistical parameters such as mean, standard deviation and relative frequency distribution of aperture are currently used to quantify the aperture geometry. A relative frequency distribution of apertures gives the different probabilities for different aperture ranges that occur on a fracture surface. Observed relative frequency density histograms, if desired, can be approximated by using different mathematical probability density functions such as normal, lognormal, gamma and beta distributions. However, simply by knowing the aperture relative frequency distribution is not sufficient to describe the entire pattern of the void geometry of a rock fracture [1]. Fractures with similar aperture frequency distributions may have different spatial correlation structures of aperture on the fracture surface. Hakami and Larsson [1] pointed out shortcomings of the aforementioned statistical parameters in capturing the complete fluid flow behavior of single fractures.

Therefore, an effective aperture characterization technique should be developed that can be used in engineering practice easily. Laboratory experiments conducted to measure fracture aperture have been reported by Gale [2], Pyrak-Nolte et al. [3], Gentier et al. [4], Hakami and Barton [5] and Iwano and Einstein [6].

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