The discrete ice lens theory of frost heave in one-dimensional soil columns was developed to provide a better physical basis for engineering predictions of frost heave in soils. The theory has now been extended to the two-dimensional heat- and mass-flow situation beneath a buried chilled pipeline. Although the frozen and unfrozen soil regions beneath a buried cold pipeline are two dimensional, and the temperature and water-flow fields are potentially complex, considerable simplifications can be made by invoking the so-called quasi-static approach for estimating temperature fields around the buried pipeline. It is proposed that the curved, quasi-static temperature profiles available from published relationships are appropriate for frost-heave predictions in the two-dimensional region beneath a pipeline. Using these curved temperature profiles in the same program and solution procedure developed previously for one-dimensional soil columns allows frost-heave predictions for a buried pipeline to be carried out with a minimum of computational effort. Therefore, the lengthy and tedious numerical procedures that have been a feature of previous attempts to model heat and mass flow and the resulting frost heave in two dimensions can be avoided. The procedure has been used to predict the frost depth and heave beneath two well-documented pipeline test sections at Calgary, Alta., and Caen, France, with very good agreement between prediction and observation. Some predictions for a practical field situation indicate the initial ground temperature plays an important role in frost heave, frost penetration, and the time at which the final ice lens forms in the freezing soil. Key words : frost heave, discrete ice lens, pipeline, segregation potential, hydraulic conductivity of frozen soil.
Two-Dimensional Modelling and Validation of the Mass Flow in a Mixing Stirred Reactor
