Fractal and multifractal analysis of fractured geological media: Surface-subsurface correlation

Computers and Geosciences

Volumn 25, Issue 9, 1999, Pages 1081-1096

  Paredes, C ^a   Elorza, F J ^a  

^a Rios R   (Spain)

Author keywords

Fracture density; Fracture media; Fracture simulation; HIDROBAP Project

Indexed keywords

FRACTAL ANALYSIS; FRACTURE GEOMETRY; FRACTURED MEDIUM; RADIOACTIVE WASTE; REPOSITORY;

EID: 0033381059     PISSN: 00983004     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0098-3004(99)00069-2     Document Type: Article

References (46)

1. Agterberg F.P., Cheng Q., Brown A., Good D. Multifractal modelling of fractures in the Lac du Bonnet batholith, Manitoba. Computers and Geosciences. 22:(5):1996;497-507.
2. Baecher G.B., Lanney N.A., Einstein H.H. Statistical description of rock properties and sampling. Proceedings of the 18th U.S. Symposium on Rock mechanics, American Institute of Mining engineers 5C1-8, Keyston, CO. 1977;501-508.
3. Barton C.C., Hsieh P.A. Physical and hydrologic flow properties of fractures. Field Trip Guide Book T385, 28th International Geological Congress AGU, Washington, DC. 1989;. 36 pp.
4. Barton C.C. Fractal analysis of scaling and spatial clustering of fractures. Barton C.C., La Pointe P.R. Fractals in the Earth Sciences. 1995;141-178 Plenum Press, New York.
5. Bear J., Tsang C.-F., Marsily G. Flow and Contaminant Transport in Fractured Rock. 1993;Academic Press, San Diego, 560 pp.
6. Bear J. Dynamics of Fluids in Porous Media. 1972;Dover Publications, New York, 764 pp.
7. Billaux D., Chiles J.P., Hestir K., Long J. Three-dimensional statistical modelling of a fractured rock mass: an example from the Fanay-Augères mine. International Journal Rock Mechanics Mining Science and Geomechanics Abstracts. 26:(3/4):1989;281-299.
8. Birkholzer J., Tsang C.-F. Solute channelling in unsaturated heterogeneous porous media. Water Resources Research. 33:(10):1997;2221-2238.
9. Bour O., Davy P. Connectivity of random fault networks following a power law fault length distribution. Water Resources Research. 33:(7):1997;1567-1583.
10. Cacas, M.-C., 1989. Developpement d'un modele tridimensionnel stochastique discret pour la simulation de l'ecoulement et des transferts de masse et de chaleur en milieu fracture. Ph.D. dissertation, Ecole Nationale Supérieure des Mines de Paris, Paris, 281 pp.
11. Carey G.F. Finite Element Modelling of Environmental Problems: Surface and Subsurface Flow and Transport. 1995;John Wiley and Sons, Chichester, 378 pp.
12. Cheng Q. Discrete multifractals. Mathematical Geology. 29:(2):1997;245-266.
13. Cheng Q. Multifractal modelling and lacunarity analysis. Mathematical Geology. 29:(7):1997;919-932.
14. Cheng Q., Agterberg F.P. Multifractal modelling and spatial point processes. Mathematical Geology. 27:(7):1995;831-845.
15. Cheng Q., Agterberg F.P. Multifractal modelling and spatial statistics. Mathematical Geology. 28:(1):1996;1-16.
16. Cheng Q., Agterberg F.P. Comparison between two types of multifractal modelling. Mathematical Geology. 28:(8):1996;1001-1015.
17. Dersowitz, W., Redus, K., Wallmann, P., Lapointe, P., Axelsson, C.-L., 1992. The implication of fractal dimension in hydrogeology and rock mechanics. Version 1.1. SKB Technical Report 92-17. Stockholm, 62 pp.
18. El Berrocal Project, 1997. Characterization and validation of natural radionuclide migration processes under real conditions on the fissured granitic environment. (European Commission Contract No. FI2W/CT91/0080), ENRESA Topical Reports 1, 2, 3, 593 pp.
19. Falconer K. Fractal Geometry. Mathematical Foundations and Applications. 1990;John Wiley and Sons, Chichester, 288 pp.
20. Falconer K. Techniques in Fractal Geometry. 1997;John Wiley and Sons, Chichester, 256 pp.
21. Feder J. Fractals. 1988;Plenum Press, New York, 283 pp.
22. Fisher N.I., Lewis T., Embleton B.J.J. Statistical Analysis of Spherical Data. 1987;Cambridge University Press, Cambridge, 329 pp.
23. Franke H.-J., Teutsch G. Stochastic simulation of regional pesticide transport including the unsaturated and the saturated zone. Ecological Modelling. 75/76:1994;529-539.
24. Gelhar L.W. Stochastic Subsurface Hydrology. 1993;Prentice Hall, New Jersey, 390 pp.
25. HIDROBAP project, 1997. Second annual activities report. Contract No. 0700443 ENRESA - Contract No. SEP/320/95/640 CSN. Madrid.
26. Huang C.-W., Shih T.-Y. On the complexity of point-in-polygon algorithms. Computers and Geosciences. 23:(1):1997;109-118.
27. Hunt F. Error analysis and convergence of capacity dimension algorithms. SIAM Journal of Applied Mathematics. 50:(1):1990;307-321.
28. Kinzelbach W. Groundwater Modelling: an Introduction with Sample Programs in Basic. 1986;Elsevier Science Publishers BV, Amsterdam, 333 pp.
29. Mandelbrot B.B. The Fractal Geometry of Nature. 1977;W.H. Freeman and Company, New York. 468 pp.
30. Mardia K.V. Statistics of Directional Data. 1972;Academic Press, London, 355 pp.
31. Margolin G., Berkowitz B., Scher H. Structure, flow, and generalized conductivity scaling in fracture networks. Water Resources Research. 34:(9):1998;2103-2121.
32. Paredes, C., 1995. Aplicación de la geometría fractal en las ciencias de la tierra. Ph.D. dissertation, Escuela Técnica Superior de Ingenieros de Minas, Universidad Politécnica de Madrid, 396 pp.
33. Paredes C., Vela A., Elorza F.J., Florez F., Mazadiego L., Llamas J.F., Pérez E., Vives L., Carrera J., Muñoz A., de Vicente G., Casquet C., Bajos C. Structural and geochemical techniques for the hydrogeological characterization and stochastic modelling of fractured media. Proceedings of the 3rd GEOTRAP Workshop on Characterization of Water-Conducting Features and their Representation in Models for Radionuclide Migration. 1998;OECD/NEA, Barcelona, 12 pp.
34. Pruess S.A. Some remarks on the numerical estimating of fractal dimension. Barton C.C., La Pointe P.R. Fractals in the Earth Sciences. 1995;65-75 Plenum Press, New York.
35. Reches Z. Determination of the tectonic stress tensor from slip along faults that obey the Coulomb yield condition. Tectonics. 7:1987;849-861.
36. Reches Z., Baer G., Hatzor Y. Constraints on the strength of the upper crust from stress inversion of fault slip data. Journal of Geophysical Research. 97:(B9):1992;12481-12493.
37. Rhén, I., Bäckbom, G., Gustafson, G., Stanfors, R., Wikberg, P., 1997. Äspö HRL: geoscientific evaluation 1997/2. Results from pre-investigations and detailed site characterization. Summary report, SKB Technical Report 97-03, 240 pp.
38. Ripley B.D. Statistical Inference for Spatial Processes. 1988;Cambridge University Press, Cambridge, 148 pp.
39. Rogers D.F. Procedural Elements for Computer Graphics. Computer Science Series. 1985;McGraw Hill, New York, 433 pp.
40. Sahimi M. Applications of Percolation Theory. 1994;Taylor and Francis, London, 258 pp.
41. Sahimi M. Flow and Transport in Porous Media and Fractured Rock. From Classical Methods to Modern Approaches. 1995;VCH, Weinheim, 482 pp.
42. Samuel, J.K., 1988. A method for estimating the Hausdorff dimension of a planar line pattern. M.Sc. thesis, Colorado School of Mines, Golden, Colorado, 51 pp.
43. Stoyan D., Stoyan H. Fractals, Random Shapes and Point Fields: Methods of Geometrical Statistics. 1994;John Wiley and Sons, Chichester, 389 pp.
44. Stoyan D., Kendall W.S., Mecke J. Stochastic Geometry and its Applications. 1987;John Wiley and Sons, Chichester, 345 pp.
45. Walsh J.J., Watterson J. Fractal analysis of fracture patterns using the standard box-counting technique: valid and invalid methodologies. Journal of Structural Geology. 15:(12):1993;1509-1512.
46. Zhang X., Sanderson D.J., Harkness R.M., Last N.C. Evaluation of the 2D permeability tensor for fractured rock masses. International Journal Rock Mechanics Mining Sciience and Geomechanics Abstracts. 33:(1):1996;17-37.