Abstract
Frost heave induced ground surface uplift can have a destructive impact on infrastructures when freezing methods are used for underground construction. The complexity of overburden pressure and the coupled heat and mass transport interaction and their relation to different water flow rates make frost heave modelling an interesting but challenging task. A frost heave model describing phase transition and multiphase interactions (liquid-crystal-soil matrix) is presented in this paper and used to investigate the kinetic growth of the ice lens. By introducing water activity determined growth rate of ice crystals, the micro- and mesophysical mechanisms underlying ice lens growth involve ice crystal nucleation, crystallization, phase transition, and water migration in the frozen fringe are explored. This work indicates that the frozen fringe thickness, the ice crystals growth and the cryogenic-suction in the frozen fringe are particularly significant in determining the ice lens growth kinetics (frost heave) under different overburden pressures. The variation in ice lens growth under various overburden pressures appears to be controlled by the water flow path, cryogenic-suction, and permeability of the frozen fringe. This research reveals the kinetic growth of the ice lens, and helps to evaluate and mitigate geological hazards when artificial ground freezing is applied.
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Abbreviations
- A 0 :
-
Pre-exponential factor related to the collision frequency in per unit volume and per unit time
- a w :
-
Water activity
- c w, c i :
-
Concentration of water and ice
- d g, σ g :
-
Geometrical mean diameter of the soil particles and standard deviation
- g :
-
Gravitational acceleration
- I(t):
-
Homogeneous nucleation rate
- κ b, R*:
-
Boltzmann constant, and ideal gas constant
- K(T k)f, K(T k)t :
-
Forward rate constant, and reverse rate constant
- L, T,T a :
-
Latent heat, temperature, and 273.15 K
- ṁ :
-
Ice-water phase transition rate
- m cl, m si :
-
Mass fraction of clay and silt
- n :
-
Soil porosity
- n m, n c :
-
Number of molecules on the surface of a nucleus, and number of supercritical nuclei
- N(t):
-
Stable nuclei number formed from the liquid phase
- n w0 :
-
Number of cooled water molecules
- n wi, n iw :
-
Material parameters related to phase transition rate
- P p, P, P i :
-
Pore pressure, water pressure, and ice pressure
- r, r c :
-
Radius of the ice embryo, and critical size of supercritical nuclei
- R :
-
Hydraulic permeability of the frozen fringe
- R sat :
-
Saturated hydraulic permeability of an unfrozen soil
- t, x :
-
Time, and position coordinate
- T k :
-
Temperature in Kelvin
- V i, V w :
-
Ice lens growth rate, and water flow rate
- v i, v w :
-
Specific volume of the ice and water
- x f :
-
Freezing front
- x w :
-
The bottom of the warmest ice lens
- α :
-
Compression coefficient of the unfrozen soil
- χ w, χ i :
-
Saturation degree of unfrozen water and ice
- Δc p :
-
Difference in specific heat capacity between water and ice
- ΔG c, ΔG 0 :
-
Energy barrier for the spontaneous formation of supercritical nuclei, and energy barrier for the diffusion of molecules
- ΔmH1(T a):
-
Molar latent heat of freezing
- λ w, λ i, λ s :
-
Heat conductivity of the water, ice, and soil
- ξ v, λ :
-
Volumetric heat capacity of the soil, and volumetric heat conductivity
- ξ w, ξ i, ξ s :
-
Volumetric specific heat capacities of water, ice, and soil
- ρ w, P i, P d :
-
Water density, ice density, and dry density of soil
- σ, σ ′ :
-
Total stress, and effective stress
- υ :
-
Collision frequency of a single molecule
- υ 0 :
-
Pre-exponential factor of collision frequency
- ψ i, ψ w :
-
Volumetric fraction of the ice, and volumetric fraction of water
- ψ sta, ψ s :
-
Saturated water content, and volume of the soil matrix
- Q, β :
-
Soil parameters dependent on the soil freezing characteristics
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Acknowledgments
This research was funded by State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining & Technology (Grant SKLGDUEK2011) and National Natural Science Foundation of China (Grant 41672343 and 41772338).
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Ji, Y., Zhou, G., Hall, M.R. et al. Thermal-Hydraulic-Mechanical Coupling Research on Overburden Pressure Mitigated Ice Lens Growth in the Freezing Soil. KSCE J Civ Eng 26, 1606–1617 (2022). https://doi.org/10.1007/s12205-022-0603-6
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DOI: https://doi.org/10.1007/s12205-022-0603-6