Minimum Scanline-to-Fracture Angle and Sample Size Required to Produce a Highly Accurate Estimate of the 3-D Fracture Orientation Distribution

Accurate estimates of the three-dimensional (3-D) rock fracture orientation distribution are crucial for generating a reliable fracture system model. Although an earlier method by Fouché and Diebolt allows one to estimate such distributions from one-dimensional (1-D) samples, this method does not typically produce highly accurate estimates of the 3-D orientation distribution (HAE3DOD). In this study, the minimum scanline-to-fracture angle ( minimum θ) and the minimum orientation sample size ( minimum n) required to produce HAE3DOD are investigated. Firstly, the factors significantly influencing minimum θ and minimum n are identified, and the influence clarified. For minimum θ, the possible influencing factors include the orientation concentration parameter ( k) and n, while for minimum n, the possible influencing factors include k and θ. Fractures from three selected sites in China provide sufficient data for this investigation. The investigation results reveal that minimum θ varies almost linearly with k and n. Moreover, minimum n varies linearly with k and θ. Variations in the minimum θ and minimum n values are strongly associated with discrepancies in sample density resulting from different values of these factors. To ease the estimation of minimum θ and minimum n, empirical relations that take into account the separate factors are proposed for these two variables. A practical example demonstrates that the proposed relations accurately and efficiently estimate minimum θ and minimum n and can provide sampling guidelines (i.e., the intervals of scanline direction and sample size) for producing HAE3DOD. The potential limitations of the proposed relations are also discussed.