饱和颗粒土一维冰分凝模型及数值模拟

THE THEORETICAL STUDY ON FROST HEAVE FOR SATURATED GRANULAR SOIL-NUMERICAL SIMULATION OF 1-D ICE SEGREGATING MODEL BASED ON EQUILIBRIUM OF FORCE AND PHASE

基于相平衡和力平衡提出了一个关于饱和颗粒土的冰分凝模型,引入了冰分凝时未冻水迁移的驱动势,基于Clapeyron方程和吸附膜的观点简要叙述了相变区内未冻水含量与温度及孔隙水压的关系,数值模拟了饱和颗粒土的一维冻结过程,得到了冰分层分凝的计算结果,与已有实验所观测到的现象较为吻合,计算所得的冻胀量的变化趋势与已有实验所测结果是相符的.

Based on the rigid ice model, a new 1-D numerical ice segregating model is developed for freezing process in saturated, granular soil. In this model, according to O＇Nell ＆ Miller＇s proposition, liquid water is attracted toward the soil grain＇s surface and the attractive force is greater for liquid than for air or ice. The strength of this attraction decays with the distance from the surface. A grain immersed in water is surrounded by a ＂hydrostatic pressure field＂ caused by this attraction. The water in the effective range of the ＂hydrostatic pressure field＂ forms socalled an adsorbed film. The water pressure in the adsorbed film is equal to the pressure caused by surface adsorption plus the porous water pressure outside the film. In unfrozen soil, grains contact each other through the adsorbed film. The pressure at the middle line of the adsorbed water film is equal to the contact stress between grains. In the saturated soil freezing process, the porous water outside the adsorbed film first freezes, then the ice-water interface gradually enters the film while the temperature drops. The adsorbed film between grains will be frozen when the temperature is less than the phase transformation temperature corresponding to the grains contact stress. According to the states of porous water and the water film between grains, the freezing soil could be divided into frozen section, phase transformation section called frozen fringe and unfrozen section. The water transferring is ignored in the frozen section and the phase-exchange does not occur in the unfrozen section. The ice segregating process could be considered as a quasi-steady process because the temperature changes slowly, so the phase and force may be assumed to be in a local equilibrium. The governing equations are deduced from the conservation of mass and energy and the relation between porosity and effective stress is considered as approximately linear. The relation between （aI/auw）T and （aI/aT）uw is deduced based on Clapeyron equation, so （aI/aT）uw could replace （aI/aT）uw in the numerical simulation. The relation between temperature T and the porous water pressure uw in the express I（T, uw） is deduced by a similar method. When the water film between soil granules begins to freeze and to separate from soil skeleton, the ice segregating process initiates. That means that the criterion of new segregated ice initiation can be stated as the maximum water pressure at ice-water interface in the frozen fringe being equal or greater than the total load. In the ice segregating process, the porous water pressure at the warm side of the warmest segregated ice drops with the temperature. Thus the moisture in the frozen fringe and unfrozen section transfers to the warm side of the segregated ice. 1-D freezing process is simulated with a similar condition as in the experiment （Xu et al., 1995）. The calculated result shows the ice layers. The trend of heave change and the distribution of ice layers are similar to those in the experiment.