The use of the Pareto distribution for fracture transmissivity assessment

For many applications data on the transmissivity distribution of individual fractures are necessary, i.e., discrete fracture network (DFN) modelling of groundwater flow and transport of solutes in fractured rock and design and performance of rock grouting. Using borehole data from the Äspö Hard Rock Laboratory, Sweden, it is shown that evaluated fracture transmissivities from three boreholes at Äspö can be well described by a Pareto or power-law distribution. Evaluated distribution parameters for the three boreholes are similar, which indicates that the Pareto distribution is a robust tool to assess three fracture transmissivity distributions. Using the evaluated distribution parameters random simulations of the original interval test data show that the approximate lognormal distributions of these are reproduced. This strengthens the credibility of the approach. It is shown how the distribution parameters can be assessed from incomplete data using the properties of the distribution. Finally, Pareto distribution transmissivities also imply Pareto distribution apertures of the fractures.