Advertisement

Mathematical Geology

, Volume 36, Issue 6, pp 683–702 | Cite as

An Algorithm for Generating Rock Fracture Patterns: Mathematical Analysis

  • Michael S. Riley
Article

Abstract

A statistical, rule-based algorithm for generating fracture patterns similar to those observed in Limestone is presented. For each fracture set, initial seed points are randomly positioned within the modelled domain with the same density as the fractures observed in the field. An orientation is associated with each point by sampling from the distribution of orientations for the corresponding fracture set. Fractures are then allowed to grow from the seed points in both directions with this orientation until they meet other fractures whereupon they continue or terminate according to a fixed probability. A mathematical analysis of this method is presented for the case in which fractures within a set are assumed to be parallel. Approximations to the distribution of semi-trace lengths are derived which are shown to be in good agreement with simulation results. Fracture spacing distributions are also derived for this case.

limestone stochastic simulation trace length fracture spacing 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. Gringarten, G., 1998, Fracnet: Stochastic simulation of fractures in layered systems: Comput. Geosci., v. 24, no. 8, p. 729–736.CrossRefGoogle Scholar
  2. Horgan, G. W., and Young, I. M., 2000, An empirical stochastic model for the geometry of twodimensional crack growth in soil (with Discussion): Geoderma, v. 96, p. 263–289.CrossRefGoogle Scholar
  3. Josnin, J.-Y., Jourde, H., Fénart, P., and Bidaux, P., 2002, A three-dimensional model to simulate joint networks in layered rocks: Can. J. Earth Sci., v. 39, p. 1443–1455.CrossRefGoogle Scholar
  4. Lloyd, J. W., Greswell, R., Williams, G. M., Ward, R. S., Mackay, R., and Riley, M. S., 1996, An integrated study of controls on solute transport in the Lincolnshire Limestone: Q. J. Eng. Geol., v. 29, no. 4, p. 321–339.Google Scholar
  5. Olsen, J. E., 1993, Joint pattern development: Effects of subcritical crack growth and mechanical crack interaction: J. Geophys. Res., v. 98, no. B7, p. 12251–12265.Google Scholar
  6. Renshaw, C. E., and Pollard, D. D., 1994, Numerical simulation of fracture set formation: A fracture mechanics model consistent with experimental observations: J. Geophys. Res., v. 99, no. B5, p. 9359–9372.CrossRefGoogle Scholar
  7. Riley, M. S., Ward, R. S., and Greswell, R. B., 2001, Converging flow tracer tests in fissured limestone: Q. J. Eng. Geol. Hydrogeol., v. 34, no. 3, p. 283–297.Google Scholar
  8. Swaby, P. A., and Rawnsley, K. D., 1996, An interactive 3D fracture modelling environment: Society of Petroleum Engineers, Tulsa, SPE 36004, Dallas, Texas, p. 177–187.Google Scholar

Copyright information

© International Association for Mathematical Geology 2004

Authors and Affiliations

  • Michael S. Riley
    • 1
  1. 1.Hydrogeology Research Group, Earth Sciences, School of Geography, Earth and Environmental SciencesUniversity of BirminghamBirminghamUnited Kingdom

Personalised recommendations