Article thumbnail
Location of Repository

Secondary frost heave in freezing soils

By C. Noon


Frost heave describes the phenomenon whereby soil freezing causes upwards surface motion due to the action of capillary suction imbibing water from the unfrozen region below. The expansion of water on freezing is a small part of the overall surface heave and it is the flow of water towards the freezing front which is largely responsible for the uplift. In this thesis, we analyse a model of frost heave due to Miller (1972, 1978) which is referred to as `secondary frost heave'. Secondary frost heave is characterised by the existence of a `partially frozen zone', underlying the frozen soil, in which ice and water coexist in the pore space. In the first part of the thesis we follow earlier work of Fowler, Krantz and Noon where we show that the Miller model for incompressible soils can be dramatically simplified. The second part of the thesis then uses this simplification procedure to develop simplified models for saline and compressible soils. In the latter case, the development of the theory leads to the consideration of non-equilibrium soil consolidation theory and the formation of segregated massive ice within permafrost. The final part of the thesis extends the simplified Miller model to the analysis of differential frost heave and the formation of patterned ground (e.g. earth hummocks and stone circles). We show that an instability mechanism exists which provides a plausible theory for the formation of these types of patterned ground

Topics: Geophysics, Partial differential equations, Approximations and expansions, Numerical analysis
Year: 1996
OAI identifier:

Suggested articles


  1. (1993). A computationally feasible reduction of the O’Neill-Miller model of secondary frost heave.
  2. (1994). A generalized secondary frost heave model.
  3. (1992). A mathematical model for compaction in sedimentary basins.
  4. (1988). A mathematical model of frost heave in granular materials.
  5. (1980). A mechanistic theory of ice lens formation in fine-grained soils.
  6. (1978). A model for coupled heat and moisture transfer during soil freezing. doi
  7. (1980). A model for frost heave including overburden. Cold Reg.
  8. (1993). A model for water transport and ice lensing in freezing soils.
  9. (1979). A model of the ‘liquid like’ layer between ice and a substrate with applications to wire regelation and particle migration.
  10. (1987). A new method for calculating frost heave including solute effects.
  11. (1993). A simplified numerical solution of the Miller model of secondary frost heave.
  12. (1993). Application of existing hypotheses used in the mathematical description of ice segregation in freezing soils.
  13. (1983). Approximate solutions for Miller’s theory of secondary heave.
  14. (1989). Basic Chemical Thermodynamics.
  15. (1931). Capillary conduction of liquids in porous mediums.
  16. (1996). Compaction, consolidation and regional groundwater flow modelling.
  17. (1992). Compositional convection and freckle formation in solidification of binary alloys.
  18. (1991). Differential frost heave, load casting and convection: Converging mechanisms; a discussion of the origin of cryoturbations. Permafrost and Periglacial Processes.,
  19. (1991). Discrete ice lens theory for frost heave in soils.
  20. (1988). Dynamics of Fluids in Porous Media.
  21. (1960). Effective stress in soils, concrete and rocks.
  22. (1990). Elementary Fluid Dynamics.
  23. (1985). Exploration of a rigid ice model of frost heave.
  24. (1984). Free and Moving Boundary Problems.
  25. (1972). Freezing and heaving of saturated and unsaturated soils.
  26. (1984). Freezing in porous media; a review of mathematical models.
  27. (1980). Freezing phenomena in soils. In
  28. (1994). Frost heave characteristics of a clayey silt subjected to small temperature gradients.
  29. (1994). Frost heave characteristics of undisturbed sensitive Champlain sea clay.
  30. (1983). Frost heave of saline soils. In
  31. (1978). Frost heaving in non-colloidal soils.
  32. (1975). Frost propagation in wet porous media. In Applications of methods of functional analysis to problems in mechanics (Joint Symposium,
  33. (1980). Fundamentals of Soil Physics.
  34. (1941). General theory of three-dimensional consolidation.
  35. (1989). Influence of overconsolidation on the freezing characteristics of clayey silt.
  36. (1993). Issues in Canadian permafrost research.
  37. (1977). Lens initiation in secondary heaving.
  38. (1992). Massive ice of the Tuktoyaktuk area, western Arctic coast,
  39. (1980). Mathematical model to correlate frost heave of pavements with laboratory predictions.
  40. (1996). Mathematical Modelling in the Applied Sciences.
  41. (1995). Mechanics of Porous Continua.
  42. (1973). Migration of mineral particles in ice with a temperature gradient. doi
  43. (1992). Modeling and experimental studies of frost heave including solute effects. Cold Reg.
  44. (1982). Numerical solutions for a rigid ice model of secondary frost heave.
  45. (1967). On the mobility of water molecules in the transition layer between ice and a solid surface.
  46. (1977). On the origin of the water aspiration in a freezing dispersed medium. doi
  47. (1988). Patterned ground. Scientific American.,
  48. (1966). Phase equilibria and soil freezing.
  49. (1973). Physics, Chemistry and Mechanics of Frozen Ground: A review.
  50. (1989). Salt redistribution during freezing of saline sand columns at constant rates.
  51. (1989). Secondary frost heave in freezing soils.
  52. (1990). Secondary frost heave in saline soils. Transfer Dissertation.
  53. (1935). Soil freezing and frost heaving with special application to roads and railroads.
  54. (1966). Soil freezing and soil water characteristic curves.
  55. (1991). Solute rejection in freezing soils.
  56. (1963). Some aspects of effective stress in saturated and partly saturated soils.
  57. (1985). Some developments of a rigid-ice model of frost heave.
  58. (1988). State of the art: Mechanical properties of frozen soil.
  59. (1978). Strength and deformation of frozen silt.
  60. (1985). The formation of freckles in binary alloys.
  61. (1989). The Frozen Earth. Fundamentals of Geocryology. doi
  62. (1991). The influence of a cubic density law on patterned ground formation.
  63. (1930). The mechanics of frost heaving. doi
  64. (1978). The Mechanics of Soils; an Introduction to Critical State Soil Mechanics.
  65. (1959). The mechanism of frost heaving in soils.
  66. (1971). The origin of massive icy beds in permafrost, western Arctic coast,
  67. (1957). The Physics of Flow through Porous Media. doi
  68. (1983). The physics of mathematical frost heave models: A review. Cold Reg.
  69. (1983). The redistribution of solutes in freezing soil: Exclusion of solutes. In
  70. (1936). The shearing resistance of saturated soil and the angle between the planes of shear.
  71. (1967). The theory of onedimensional consolidation of saturated clays.
  72. (1961). The thermodynamics of frost damage to porous solids.
  73. (1976). Theoretical analysis of convective instability of a growing horizontal thermal boundary layer. The Physics of Fluids., doi
  74. (1955). Theory of elasticity and consolidation for a porous anisotropic solid.
  75. (1978). Thermodynamic equilibrium between ice and water in porous media.
  76. (1990). Three functions that model empirically measured unfrozen water content data and predict relative hydraulic conductivity.
  77. (1995). Validation of a Fully Predictive Model for Secondary Frost Heave. Arctic and Alpine Research.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.