The theoretical exploration of frost heave for saturated granular soil--numerical simulation of 1-D ice segregating model based on equilibrium of force and phase

Based on the theory in the rigid ice model, a new 1-D numerical icesegregating model is developed for freezing process in saturated, granularsoil. In this model according as O'Nell \& Miller' proposition, liquidwater is attracted toward the soil grain's surface and the attractive forceis greater for liquid than for air or ice. The strength of this attractiondecays with distance from the surface. A grain immersed in water issurrounded by a ``hydrostatic pressure field'' caused by this attraction.The water in the effective range of the ``hydrostatic pressure field''called adsorbed film. The water pressure in adsorbed film is equal to thepressure caused by surface adsorption plus the porous water pressure outsidethe film. In unfrozen soil, grains contact to each other through theadsorbed film. The pressure at the middle line of the adsorbed water film isequal to the contact stress between grains. In the saturated soil freezingprocess, the porous water outside the adsorbed film first freeze, then theice-water interface gradually enter into the film with the temperature drop.The adsorbed film between grains will be frozen while the temperature isless than the phase changing temperature corresponding to the grains contactstress. According to the states of porous water and the water film betweengrains, the freezing soil could be divided into frozen section, phasechanging section that called frozen fringe and unfrozen section. The watertransferring is ignored in frozen section and the phase-exchange not occursin unfrozen section. The ice segregating process could be considered as aquasi-steady process because that the temperature change slowly, then theassumption that phase and force are local equilibrium could be introduced.The governing equations are deduced from conservation of mass and energy andthe relation of porosity and effective stress is considered as approximatelinear. The relation of ( \partial I /\partialu_w )_T and ( \partial I / \partial T )_u_w is deduced based onClapeyron equation then ( \partial I / \partial T )_u_w could takeplace of ( \partial I / \partial T )_u_w in numerical simulation. Therelation of temperature T and the porouswater pressure u_w in the express I(T,u_w ) is deducedby similar method. When the water film between soil granules begins tofreeze to separate soil skeleton, ice segregating process initiated. Thatmeans the criterion of new segregated ice initiation is that the maximumwater pressure at ice-water interface in the frozen fringe become equal orgreater than the total load. In the ice segregating process, the porouswater pressure at the warm side of the warmest segregated ice drop with thetemperature lower. Thus cause that the moisture in the frozen fringe andunfrozen section transfer to the warm side of the segregated ice.1-D freezing process was simulated with similar condition to theexperiment (Xu et al., 1995). The calculated result showed the ice layers. Thetrend of heave change and the distribution of ice layers are similar to theexperiment phenomena.