The geometry of rock discontinuities plays a crucial role in permeability of fractured rock. However, exact determination of the fracture system is not possible due to the high scale dependency of the system. Often only limited data are available from core samples, outcrop analogues and seismic surveys. This research is intended to evaluate the scale effects on permeability in fractured rock mass using Oda’s permeability tensor and Monte Carlo simulation. Power law and Fisher distributions are used to generate realistic fractured rock sample in the simulations. Fracture distribution is related with permeability distribution in the first part of the research, and analysis on permeability variations in different volume scales and fracture sampling ratios is conducted. The above comparison and analysis results yield the possible fracture geometry and permeability relationship without requiring redundant calculation. The permeability distribution from different sampling volume ratios shows the expected tendency in the specific range of volume ratio, determined by intensity of fracture. In the last part of the report, proportional contribution of fracture length distribution is also examined, and compared with the above result.


Determination of fractured rock mass permeability is the most important issue in different fields, such as ground water flow modeling, contaminant flow and transport, and hydrocarbon production. In most cases, permeability of the fracture path is much larger than the permeability of the intact rock masses [1, 2]. Therefore, understanding the system of the fracture is the most important part in determing the permeability of fractured rock masses. However, it is impossible to consider every single fracture in numerical analysis, because the fracture sets are not only very complicated, but also site and scale specific. To account for every fracture in a fractured rock mass will be computationally prohibitive. Due to these difficulties, extensive research efforts have been made to develop effective methods to analyze and calculate fractured rock permeability.

Since 1960s, explicit and discrete fracture and matrix models have been utilized by many researchers, for example by Snow [3], Stothoff [4] and Min et al [2]. The dual continuum method, including double porosity and dual permeability, have been developed and used by Barenblatt et al [5], Warren and Root [6], Kazemi [7], Pruess and Narasimhan [8], and Wu and Pruess [9]. Oda [1] developed a crack and permeability tensor method which considers the volume fraction of fracture set inside of the whole fractured rock domain. In his model, a crack tensor is formulated based on the assumption that a fractured rock mass can be assumed to be a homogeneous, anisotropic porous medium. The permeability tensor of fractured rock sample can be calculated by the crack tensor with the geometrical characteristics of a fracture set such as length, aperture, and orientation.

In this research, the effects of fracture geometry and length scale on permeability are reviewed by the use of analytical permeability tensor model developed by Oda [1]. Monte Carlo Simulation (MCS) technique is adopted in order to stochastically generate realistic fracture geometries.

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