Abstract
Little consensus exists on how best to analyze natural fracture spacings and their sequences. Field measurements and analyses published in geotechnical literature imply fracture processes radically different from those assumed by theoretical structural geologists. The approach adopted in this paper recognizes that disruption of rock layers by layer-parallel extension results in two spacing distributions, one representing layer-fragment lengths and another separation distances between fragments. These two distributions and their sequences reflect mechanics and history of fracture and separation. Such distributions and sequences, represented by a 2 × nmatrix of lengths L,can be analyzed using a method that is history sensitive and which yields also a scalar estimate of bulk extension, e(L).The method is illustrated by a series of Monte Carlo experiments representing a variety of fracture-and-separation processes, each with distinct implications for extension history. Resulting distributions of e(L) are process-specific, suggesting that the inverse problem of deducing fracture-and-separation history from final structure may be tractable.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ashton, W. D., 1971, Distributions for gaps in road traffic: Jour. Inst. Math. Appl., v. 7, p. 37–46.
Beloussov, V. V., 1952, Spacing of fracture in rocks: Akad. Nauk SSSR Trad. Geofiz. Inst. v. 17, p. 144.
Biot, M. A., 1965, Mechanics of incremental deformation: John Wiley & Sons, New York, 519 p.
Bridges, M. C., 1975, Presentation of fracture data for rock mechanics: 2nd Australia—New Zealand Conference on Geomechanics, Institute of Engineers, Australia, National Conference Publication 75/4, p. 144–148.
Chadwick, P. K., 1975, A psychological analysis of observation in geology: Nature, London, v. 256, p. 570–573.
Chatfield, C., 1978, Statistics for technology (2nd ed.): Chapman and Hall, London, 370 p.
Chertkova, E. I., 1950, Some results of the modeling of tectonic faults: Akad. Nauk SSSR Izv. Ser. Geol. 14, no. 5, p. 42–44.
Chinnery, M. A., 1966, Secondary faulting: Can. Jour. Earth Sci., v. 3, p. 163–174.
Cobbold, P. R. and Ferguson, C. C., 1979, Description and origin of spatial periodicity in tectonic structures: Report on a Tectonic Studies Group Conference held at Nottingham University, 8 November 1978: Jour. Struct. Geol., v. 1, no. 1, p. 93–97.
Cox, H. L., 1952, The elasticity and strength of paper and other fibrous materials: Br. Jour. Appl. Phys., v. 3, p. 72–79.
Deere, D. U., 1963, Technical description of rock cores for engineering purposes: Rock Mech. Engr. Geol., v. 1, p. 16–22.
Ferguson, C. C., 1981, A strain reversal method for estimating extension from fragmented rigid inclusions: Tectonophysics, v. 79, p. T43-T52.
Ferguson, C. C. and Lloyd, G. E., 1984, Extension analysis of stretched belemnites: A comparison of methods: Tectonophysics, v. 101, p. 199–206.
Fletcher, R. C. and Hallet, B., 1983, Unstable extension of the lithosphere: A mechanical model for Basin-and-Range structure: Jour. Geophys. Res., v. 88, no. B9, p. 7457–7466.
Harris, S. F., Taylor, G. L., and Walper, J. J., 1960, Relation of deformational fractures in sedimentary rocks to regional and local structure: Amer. Assoc. Petrol. Geol. Bull., v. 44, p. 1853–1873.
Hobbs, D. W., 1967, Formation of tension joints: Geol. Mag., v. 104, p. 550–556.
Hudson, J. A. and Priest, S. D., 1979, Discontinuities and rock mass geometry: Int. Jour. Rock Mech. Min. Sci. Geomech. Abstr., v. 16, p. 339–362.
Hudson, J. A. and Priest, S. D., 1983, Discontinuity frequency in rock masses: Int. Jour. Rock Mech. Min. Sci. Geomech. Abstr., v. 20, p. 73–89.
Kelly, A., 1973, Strong solids: Clarendon Press, Oxford, 230 p.
Lachenbruch, A. H., 1961, Depth and spacing of tension cracks: J. Geophys. Res., v. 66, p. 4273–4292.
Lloyd, G. E., Ferguson, C. C., and Reading, K., 1982, A stress-transfer model for the development of extension fracture boudinage: Jour. Struct. Geol., v. 4, no. 3, p. 355–372.
Marsaglia, G., MacLaren, M. D., and Bray, T. A., 1964, A fast procedure for generating normal random variables: Comm. Assoc. Comput. Mach., v. 7, p. 4–10.
Merino, E., Ortoleva, P. and Strickholm, P., 1983, Generation of evenly-spaced pressuresolution seams during (late) diagenesis: A kinetic theory: Contr. Min. Pet. v. 82, p. 360–370.
Merzer, A. M. and Freund, R., 1976, Equal spacing of strike-slip faults: Geophys. Jour. Roy. Astr. Soc., v. 45, p. 177–188.
Paterson, M. S., 1978, Experimental rock deformation—The brittle field: Springer-Verlag, New York, 254 p.
Piteau, D. R., 1973, Characterizing and extrapolating rock joint properties in engineering practice: Rock Mech., Supl. 2, p. 5–31.
Priest, S. D. and Hudson, J. A., 1976, Discontinuity spacings in rock: Int. Jour. Rock Mech. Min. Sci. Geomech. Abstr., v. 13, p. 135–148.
Pyke, R., 1965, Spacings (with Discussion): Jour. Roy. Stat. Soc. Ser. B., v. 27, p. 395–449.
Ramberg, H. 1955, Natural and experimental boudinage: Jour. Geol., v. 63, p. 512–526.
Rudnicki, J. W., 1980, Fracture mechanics applied to the Earth's crust: Ann. Rev. Earth Planet. Sci., v. 8, p. 489–525.
Secor, D. T., 1968, Mechanics of natural extension fracture:in Baer, A. J. and Norris, D. K. (Eds.), Conference on Tectonics, Can. Geol. Surv. Paper 68-52, p. 3–48.
Seidensticker, C. M., Oldow, J. S., and Ave Lallement, H. G., 1982, Development of beddingnormal boudins in the Pilot Moutains, Nevada: Tectonophysics v. 90, p. 335–349.
Smith, R. B., 1975, Unified theory of the onset of folding, boudinage, and mullion structure: Geol. Soc. Amer. Bull., v. 86, p. 1601–1609.
Smith, R. B., 1977, Formation of folds, boudinage, and mullions in non-Newtonian materials: Geol. Soc. Amer. Bull., v. 88, p. 312–320.
Snow, D. T., 1968, Rock fracture spacings, openings and porosities: Proc. Amer. Soc. Civ. Engr. Soil. Mech. Found. Div., v. 94, p. 73–91.
Sowers, G. M., 1972, Theory of spacing of extension fracture:in Pincus, H. (Ed), Geological factors in rapid excavation; Geol. Soc. Amer. Engr. Geol. (case history no. 9), p. 27–53.
Stearns, D. W., 1968, Fracture as a mechanism of flow:in Baer, A. J. and Norris, D. K. (Eds.), Conference on tectonics: Can. Geol. Surv. Paper 68-52, p. 79–95.
Wallis, P. F. and King, M. S., 1980, Discontinuity spacings in a crystalline rock: Int. Jour. Rock Mech. Min. Sci. Geomech. Abstr., v. 17, p. 63–66.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ferguson, C.C. Spatial analysis of extension fracture systems: A process modeling approach. Mathematical Geology 17, 403–425 (1985). https://doi.org/10.1007/BF01032930
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01032930