Hydraulic anisotropy of homogeneous soils and rocks: influence of the densification process

  • Robert P. Chapuis
  • Denis E. Gill


Many values of the ratio kmax/kmin are available for clays and rocks which can be cut for tests in different directions. In comparison, few reliable results are available for non-cohesive materials. The hydraulic anisotropy ratios of homogeneous clays, rocks and granular soils appear to be very similar. In particular, kmax/kmin seems to be lower than 4, which confirms that this ratio has an upper limit related to the shape of particles, their arrangement, or the directional tortuosity within the pore space. In the bedding plane of sedimentary rocks, the ratio kb.max/kb.min is usually lower than 1.5, thus these rocks are nearly isotropic in their bedding plane. In granular soils, the kh/kv, contrary to common opinion, is not always higher than 1. Experimental values for sands and gravels are in the 0.75 to 4.1 range. The influence of densification on hydraulic anisotropy is found to be similar for a sand and a clay, and probably for any soil having settled in still water and influenced subsequently only by gravity. The hydraulic anisotropy of sandstone is found to be in continuity with that of sand, and it increases with densification.

Key words

soil rock permeability anisotropy densification Mots clés sol roche perméabilité anisotropie densification 

Anisotropie hydraulique des sols et roches homogènes: influence de la densification


De nombreuses valuers du rapport kmax/kmin sont disponibles pour les argiles et les roches, taillables pour des essais dans différentes directions. Comparativement, il y a peu de résultats fiables pour les matériaux sans cohésion. Les coefficients d'anisotropie hydraulique des argiles, roches et sols grenus homogènes paraissent très semblables. En particulier, kmax/kmin semble inférieur à 4, ce qui confirme que ce rapport a une limite supérieure dictée par la forme des particules, leur arrangement, ou la tortuosité directionnelle dans l'espace des vides. Dans le plan de stratification des roches sédimentaires, le rapport d'anisotropie kb.min/kb.min est généralement inférieur à 1.5, donc ces roches sont à peu près isotropes dans ce plan. Dans les sols grenus, le rapport kh/kv, contrairement à une opinion courante, ne dépasse pas toujours 1. Les valuers expérimentales pour des sables et graviers vont de 0.75 à 4.1. On trouve que la densification influence le rapport d'anisotropie de la même façon pour un sable, une argile, et probablement pour tout sol déposé en eau immobile, et densifié ensuite par la gravité seulement. L'anisotropie hydraulique du grès s'avère être en continuité avec celle du sable, et elle augmente avec la densification.


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  1. AL-TABBAA, A. and WOOD, D.M., 1987: Some measurements of the permeability of kaolin.Géotechnique, 37 (4), pp. 499–503.CrossRefGoogle Scholar
  2. AMERICAN PETROLEUM INSTITUTE, 1956: Recommended practice for determining permeability of porous media.API RP 27, 27 pp.Google Scholar
  3. ARNOLD, M.D., GONZALEZ, H.J. and CRAWFORD, P.B., 1962: Estimation of reservoir anisotropy from production data.Journal of Petroleum Technology, August, pp. 909–912.CrossRefGoogle Scholar
  4. ASTM D 2434-68 (Reapproved 1974): Standard test method for permeability of granular soils (constant head).Annual Book of ASTM Standards, Vol. 04.08, Soil and Rock; Building Stones, 1 078 p.Google Scholar
  5. ASTM D 4525-85: Standard test method for permeability of rocks by flowing air.Annual Book of ASTM Standards, Vol. 04.08, Soil and Rock; Building Stones, 1 078 p.Google Scholar
  6. BALLIVY, G., LANDANYI, B. and GILL, D.E., 1976: Effect of water saturation history on the strength of low-porosity rocks. In Soil Specimen Preparation for Laboratory Testing, ASTM STP 599, American Society for Testing and Materials, pp. 4–20.Google Scholar
  7. BASAK, P. and ANANDAKRISHNAN, M., 1970: Depth dependent hydraulic conductivity.Soil Science, 109 (6), pp. 351–355.CrossRefGoogle Scholar
  8. BASAK, P., 1972: Soil structure and its effects on hydraulic conductivity.Soil Science, 114 (6), 417–422.CrossRefGoogle Scholar
  9. BAZETT, D.J. and BRODIE, A.F., 1961: A study of matabitchuan varved clay.Ontario Hydro Research News, 13 (4), pp. 1–6.Google Scholar
  10. BERNAIX, J., 1967: Etude géotechnique de la roche de Malpasset. Dunod, Paris, 215 p.Google Scholar
  11. BOWLES, J.E., 1970: engineering properties of soils and their measurement. Chap. 11, McGraw Hill, New York, 187 p.Google Scholar
  12. CASAGRANDE, L. and POULOS, S.J., 1969: On the effectiveness of sand drains.Canadian Geotechnical Journal, 6 (3), 287–326.CrossRefGoogle Scholar
  13. CEDERGREN, H.R., 1974: Drainage of highway and airfield pavements. John Wiley & Sons, New York, 285 p.Google Scholar
  14. CHAN, H.T. and KENNEY, T.C., 1973: Laboratory investigation of permeability ratio of New Liskeard varved clay.Canadian Geotechnical Journal, 10 (3), pp. 453–472.CrossRefGoogle Scholar
  15. Chapuis, R.P., Baass, K. and Davenne, L., 1989a: Granular soils in rigid-wall permeameters: method for determining the degree of saturation.Canadian Geotechnical Journal, 26 (1), in print.CrossRefGoogle Scholar
  16. CHAPUIS, R.P., GILL, D.E. and BAASS, K., 1989b: Influence of the compaction method on the hydraulic anisotropy of a sand. Submitted for publication to theCanadian Geotechnical Journal.Google Scholar
  17. DE BOODT, M.F. and KIRKHAM, Don., 1953: Anisotropy and measurement of air permeability of soil clods.Soil Science, 76, pp. 127–133.CrossRefGoogle Scholar
  18. DESBARATS, A.J., 1987: Numerical simulation of effective permeability in sand-shale formations.Water Resources Research, 23 (2), pp. 273–286.CrossRefGoogle Scholar
  19. DUPUY, M. and LEFEBVRE Du PREY, E., 1968: L'anisotropie d'écoulement en milieu poreux présentant des intercalations horizontales discontinues.Comptes rendus du 3 Colloque de l'Association de recherche sur les techniques de forage et de production (ARTFP), Pau, Editions Technip.Google Scholar
  20. EVANS, H.E., 1962: A note on the average coefficient of permeability for a stratified soil mass.Géotechnique, 12, pp. 145–146.CrossRefGoogle Scholar
  21. FANCHER, G.H., LEWIS, J.A. and BARNES, K.B., 1933: Physical tests and properties of oil and gas sands.Proceedings of the Ist International Congress of Petroleum, London, Vol. 1, pp. 322–333.Google Scholar
  22. FERRANDON, J., 1948: Les lois d'écoulement de filtration.Le Génie Civil, 125 (2), pp. 24–28.Google Scholar
  23. FETTKE, C.R., 1938: The Bradford oil field, Pennsylvania and New York.Pennsylvania Geological Surveys, 4th Series, Bulletin M-21.Google Scholar
  24. FONTUGNE, D., 1969: Permeability measurement in anisotropic media. M.S. Thesis, Department of Chemical Engineering and Metallurgy, Syracuse University.Google Scholar
  25. GARGA, V.K., 1988: Effect of sample size on consolidation of a fissured clay.Canadian Geotechnical Journal, 25 (1), pp. 76–84.CrossRefGoogle Scholar
  26. GRAY, D.H., FATT I. and BERGAMINI, G., 1963: The effect of stress on permeability of sandstone cores.Society of Petroleum engineers Journal, 3 (2), pp. 95–100.CrossRefGoogle Scholar
  27. GREENKORN, R.A., JOHNSON, C.R. and SHALLENBERGER, L.K., 1964: Directional permeability of heterogeneous anisotropic porous media.Society of Petroleum Engineers Jounal, 4 (2), pp. 124–132.CrossRefGoogle Scholar
  28. GRIFFITHS, J.C., 1950: Directional permeability and dimensional orientation in Bradford sand.Producers Monthy., 14 (8), pp. 26–32.Google Scholar
  29. HALEY and ALDRICH, 1969: Report No. 1—Engineering properties of foundation soils at Long Creek—Fore river areas and Back Cove. Report to Maine State Highway Commission.Google Scholar
  30. HANTUSH, M.S., 1996a: Analysis of data from pumping tests in anisotropic aquifers.Journal of Geophysical Research, 71, pp. 421–426.CrossRefGoogle Scholar
  31. HANTUSH, M.S., 1966b: Wells in homogeneous anisotropic aquifers.Water Resources Research, 2, pp. 273–279.CrossRefGoogle Scholar
  32. HANTUSH, M.S. and THOMAS, R.G., 1966: A method for analyzing a drawdown test in anisotropic aquifers.Water Resources Research, 2, pp. 281–285.CrossRefGoogle Scholar
  33. HSIEH, P.A. and NEUMAN, S.P., 1985: Field determination of the three-dimensional hydraulic conductivity tensor of anisotropic media—Part 1 Theory.Water Resources Research, 21 (11), pp. 1655–1665.CrossRefGoogle Scholar
  34. HUGHES, R.V., 1951: Directional permeability trends.Proceedings of the 3rd International Congress of Petroleum.Google Scholar
  35. HVORSLEV, J., 1951: Time lag and soil permeability in ground-water observations. Bulletin No. 36, U.S. Waterways Experiment Station, Vicksburg, Miss., 50 p.Google Scholar
  36. IRMAY, S., 1951: Darcy law for non-isotropic soils. Comptes rendus de l'Assemblée Générale de Bruxelles.Association International d'Hydrologie Scientifique (UGGI) 2, p. 178.Google Scholar
  37. JAKOBSON, B., 1955: Isotropy of clays.Géotechniques, 5 (1), pp. 23–28.CrossRefGoogle Scholar
  38. JOHNSON, W.E. and HUGHES, R.V., 1948: Directional permeability measurements and their significance.Producers Monthly, 13 (1), pp. 17–25.Google Scholar
  39. JOHNSON, W.E. and BRESTON J.N., 1951: Directional permeability measurements on oil sandstones from various states.Producers Monthly, 15 (4), pp. 10–19.Google Scholar
  40. KENNEY, T.C., 1963: Permeability ratio of repeatedly layered soils.Géotechnique, 13 (4), pp. 325–333.CrossRefGoogle Scholar
  41. KENNEY, T.C. and CHAN, H.T., 1973: Field investigation of permeability ratio of New Liskeard varved clay.Canadian Geotechnical Journal, 10 (3), pp. 473–488.CrossRefGoogle Scholar
  42. LARSSON, R., 1981: Drained behavior of Swedish clays.Swedish Geotechnical Institute, Report No. 12, 157 p.Google Scholar
  43. LATINI, R.G., 1967: Measurement of directional permeabilities. M.S. Thesis, Department of Chemical Engineering and Metallurgy, Syracuse University.Google Scholar
  44. LIAKOPOULOS, A.C., 1965a: Darcy's coefficient of permeability as symetric tensor of second rank.Bulletin of the International Association of Scientific Hydrology, 10 (3), pp. 41–48.CrossRefGoogle Scholar
  45. LIAKOPOULOS, A.C., 1965b: Variation of the permeability tensor ellipsoid in homogeneous anisotropic soils.Water Resources Research, 1, pp. 135–141.CrossRefGoogle Scholar
  46. LUMB, P. and HOLT, J.K., 1968: The undrained shear strength of a soft marine clay from Hong Kong.Géotechnique, 18 (1), pp. 25–36.CrossRefGoogle Scholar
  47. MASLAND, M., 1957: Soil anisotropy and land drainage. In Drainage of agricultural lands, J.N. Luthin Editor, American Society of Agronomy, Madison, Wisconsin, pp. 216–285.Google Scholar
  48. MASLAND, M. and KIRKHAM, D., 1955: Theory and measurement of anisotropic air permeability in soil.Proceedings of the Soil Science Society of America, 19 (4), pp. 395–400.CrossRefGoogle Scholar
  49. MacGARY, L.M. and LAMBERT, T.W., 1962: Reconnaissance of ground-water resources of the Jackson Purchase region, Kentucky.U.S. Geological Survey Hydrologic Atlas 13.Google Scholar
  50. MANSUR, C.I. and DIETRICH, R.S., 1965: Pumping tests to determine permeability ratio.ASCE Journal of the Soil Mechanics and Foundation Division, 91 (SM4), pp. 151–183.Google Scholar
  51. MARCUS, H., 1962: The permeability of a sample of an anisotropic porous medium.Journal of Geophysical Research, 67 (13), pp. 5215–5225.CrossRefGoogle Scholar
  52. MARCUS, H. and EVENSON, D.E., 1961: Directional permeability in anisotropic porous media.,Water Resources Center Contribution No. 31, University of California, Berkeley, 105 pages.Google Scholar
  53. MATHERON, G., 1966: Structure et composition des perméabilités.Revue de l'Institut Français des Pétroles, 21 (4), pp. 564–580.Google Scholar
  54. MATHERON, G., 1967: Composition des perméabilités en milieu poreux hétérogène: méthode de Schwydler et règles de pondération.Revue de l'Institut Français des Pétroles, 22 (3), pp. 443–466.Google Scholar
  55. MATHERON, G., 1968: Composition des perméabilités en milieu poreux hétérogène: critique de la règle de pondération géométrique.Revue de l'Institut Français des Pétroles, 23 (2), pp. 201–218.Google Scholar
  56. MITCHELL, J.K., 1956: The fabric of natural clays and its relation to engineering properties.Proceedings Highway Research Board, 35, pp. 693–713.Google Scholar
  57. MOORE, P.J., 1979: Determination of permeability anisotropy in a two-way permeameter.Geotechnical Testing Journal, 2 (3), pp. 167–169.CrossRefGoogle Scholar
  58. MORGENSTERN, N.R. and TCHALENKO, J.S., 1967: The optical determination of preferred orientation in clays and its application to the study of microstructure in consolidated kaolin.Proceedings of the Royal Society, London, A300, (I) pp. 218–234, (II) pp. 235–250.CrossRefGoogle Scholar
  59. MORRIS, D.A. and JOHNSON, A.I., 1967: Summary of hydrologic and physical properties of rock and soil materials, as analyzed by the Hydrologic Laboratory of the U.S. Geological Survey 1948–60.Geological Survey Water-Supply Paper 1839-D, 42 p.Google Scholar
  60. MUALEM, Y., 1984: anisotropy of unsaturated soils.Soil Science Society of America Journal, 48 (3), pp. 505–509.CrossRefGoogle Scholar
  61. MUSKAT, M., 1937: The flow of homogeneous fluids through porous media. McGraw-Hill, New York, 763 p.Google Scholar
  62. NIELSEN, D.R., VAN GENUCHTEN, M.Th. and BIGGAR, J.W., 1986: Water flow and solute transport processes in the unsaturated zone.Water Resources Research, 22 (9), pp. 89S-108S.CrossRefGoogle Scholar
  63. OLSEN, H.W., 1962: Hydraulic flow through saturated clays.Proceedings of the 9th National Conference on Clay and Clay Minerals. pp. 131–161.CrossRefGoogle Scholar
  64. OLSON and DANIEL, 1981: Measurement of the hydraulic conductivity of fine-grained soils. In Permeability and Groundwater Contaminant Transport, STP 746, pp. 18–64.Google Scholar
  65. PARÉ, J.J., ARES, R., CABOT, L. and GARZON, M., 1982: Large scale permeability and filter tests at LG3.Proceedings of the XIVth Congress on Large Dams Rio de Janeiro Q. 55, R.7, pp. 103–122.Google Scholar
  66. PARSONS, R.W., 1964: Directional permeability of heterogeneous anisotropic porous media: Discussion.Society of Petroleum Engineers Journal, 4 (4), pp. 363–364.Google Scholar
  67. PIERSOL, R.J., WORKMAN, L.E. and WATSON, M.C., 1940: Porosity, total liquid satructuration, and permeability of Illinois oil sands.Illinois Geological Surveys Report of Investigations No. 67.Google Scholar
  68. REEVE, R.C. and KIRKHAM, D., 1951: Soil anisotropy and some field methods for measuring permeability.Transactions, American Geophysical Union, 32 (4), pp. 582–590.CrossRefGoogle Scholar
  69. RICE, P.A., FONTUGNE, D.J. LATINI, R.G. and BARDHUN, A.J., 1970: Anisotropic permeability in porous media.Industrial and Engineering Chemistry, 62 (6), pp. 23–31.CrossRefGoogle Scholar
  70. RIMA, D.R., MEISLER, H. and LONGWILL, S., 1962: Geology and hydrology of the Stockton Formation in southeastern Pennsylvania,Pennsylvania Topographic and Geological Survey Ground-Water Report W-14.Google Scholar
  71. RÜHL, W. and SCHMID, C., 1957: Uber das verhaltnis der vertikalen zur horizontalen absoluten Permeabilitat von Sandsteinen.Geologisches Jahrbuch, 74, pp. 447–461.Google Scholar
  72. SCHEIDEGGER, A.E., 1957: The physics of flow through porous media. University of Toronto Press, Toronto, 236 p.Google Scholar
  73. SCHEIDEGGER, A.E., 1974: The physics of flow through porous media, 3rd edition. University of Toronto Press, Toronto, 353 p.Google Scholar
  74. SCHNEEBELI, G., 1966: Hydraulique souterraine. Eyrolles, 362 p.Google Scholar
  75. SHIELDS, D.H. and ROWE, P.W., 1965: Radial drainage oedometer for laminated clays.ASCE Journal of the Soil Mechanics and Foundation Division, 91 (SMI), pp. 15–23.Google Scholar
  76. SNOW, D.T., 1968: Rock fracture spacings, openings, and porosities.ASCE Journal of the Soil Mechanics and Foundations Division 94 (SMI), pp. 73–91.Google Scholar
  77. STEWART, J.W., 1964: Infiltration and permeability of weathered crystalline rocks, Georgia Nuclear Laboratory, Dawson County, Georgia, U.S.Geological Survey Bulletin 1133-D.Google Scholar
  78. STONE, R. and SNOEBERGER, D.F., 1977: Cleat orientation and areal hydraulic anisotropy of Wyoming coal aquifer.Ground Water, 15 (6), pp. 434–438.CrossRefGoogle Scholar
  79. STONER, J.D., 1981: Horizontal anisotropy determining by pumping in two Powder River basin coal aquifers, Montana.Ground Water 19 (1), pp. 39–40.CrossRefGoogle Scholar
  80. STUART, W.T., BROWN, E.A. and RHODEHAMEL, E.C., 1954: Groundwater investigations of the Marquette Iron-Mining District.Michigan Geological Survey Technical Report No. 3.Google Scholar
  81. SUBBARAJU, B.H., NATARAJAN, T.K. and BHANDARI, R.K., 1973: Field performance of drain wells designed expressly for strength gain in soft marine clays.Proceedings of the 8th International Conference on Soil Mechanics and Foundation Enginering, Moscow, Vol. 2.2, pp. 217–220.Google Scholar
  82. SULLIVAN, R.R., 1941: Further study of the flow of air through porous media.Journal of Applied Physics, 12, pp. 503–508.CrossRefGoogle Scholar
  83. TAVENAS, F., JEAN, P., LEBLOND, P. and LEROUEIL, S., 1983: The permeability of natural soft clays. Part 11: Permeability characteristics.Canadian Geotechnical Journal, 20, pp. 645–660.CrossRefGoogle Scholar
  84. TERZAGHI, K., 1943: Theoretical soil mechanics, John Wiley, New York, 510 p.CrossRefGoogle Scholar
  85. TSIEN, S.I., 1955: Stabilization of marsh deposit.Highway Research Board Bulletin, 115, pp. 31–43.Google Scholar
  86. VREEDENBURGH C.G.F., 1936: On the steady flow of water percolating through soil with homogeneous anisotropic permeability.Proceedings of the 1st International Conference on Soil Mechanics and Foundation Engineering, Cambridge, Mass. Vol. 1, pp. 222–225.Google Scholar
  87. WEEKS, E.P., 1969: Determining the ratio of horizontal to vertical permeability by aquifer-test analysis.Water Resources Research. 5 (1), pp. 196–214.CrossRefGoogle Scholar
  88. WILKINSON, W.B. and SHIPLEY, E.L., 1969: Vertical and horizontal laboratory permeability measurements in clay soils.Proceedings of the 1st International Symposium on the Fundamentals of Transport Phenomena in Porous Media, Technion City, Haifa, Israel pp. 285–298.Google Scholar
  89. WIT, K.E., 1966: Apparatus for measuring hydraulic conductivity of undisturbed soil samples.ASTM STP 417, pp. 72–83.Google Scholar
  90. WITT, K.J. and BRAUNS, J., 1981: Durchlassigkeitsanisotropie von Haufwerken infolge Kornplattigkeit und Kornorienterung.Series of the Institute of Soil and Rock Mechanics, University of Karlsruhe, Federal Republic of Germany, No 87, pp. 81–113.Google Scholar
  91. WITT, K.J. and BRAUNS, J., 1983: Permeability anisotropy due to particle shape.Journal of Geotechnical Engineering, 109 (9), pp. 1181–1187.CrossRefGoogle Scholar
  92. WU, T.H., CHANG, N.Y. and ALI, E.M., 1978: Consolidation and strength properties of a clay.Journal of Geotechnical Engineering, 104 (GT7), pp. 889–905.Google Scholar
  93. WYLLIE, M.R.J. and ROSE, W.D., 1950: Application of the Kozeny equation to consolidated porous media.Nature, 165, p. 972.CrossRefGoogle Scholar
  94. YANG, S.T., 1948: On the permeability of homogeneous anisotropic soils.Proceedings of the 2nd International Conference on Soil Mechanics and Foundation Enginering, Rotterdam, Vol. 2. pp. 317–320.Google Scholar
  95. YOKOTA, J., 1963: Experimental studies on the design of grouting curtain and drainage for the Kurobe No. 4 Dam.Rock Mechanics Engineering Geology, 1, pp. 104–110.Google Scholar
  96. YOUNG, A., LOW, P.F. and McLATCHIE, A.S., 1964: Permeability studies of argillaceous rocks.Journal of Geophysical Research, 69, pp. 4237–4245.CrossRefGoogle Scholar
  97. ZIMMIE, T.F., DOYNOW, J.S. and WARDELL, J.T., 1981: Permeability testing of soils for hazardous waste disposal sites.Proceedings of the Xth International Conference on Soil Mechanics and Foundation Engineering, Stockholm, Vol. 2, pp. 403–406.Google Scholar

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© International Association of Engineering Geology 1989

Authors and Affiliations

  • Robert P. Chapuis
    • 1
  • Denis E. Gill
    • 1
  1. 1.Départment de Génie minéralEcole Polytechnique de MontréalMontréalCanada

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