Multiphase Approach to Thaw Subsidence of Unsaturated Frozen Soils: Equation Development

Abstract

Construction and maintenance of engineering structures in arctic regions demands an understanding of and the ability to cope with environmental problems produced by permafrost. Where thawing of the permafrost cannot be prevented, the range, amount, and extent of degradation are factors that must be taken into account in the design of engineering structures. Predictions of these factors are facilitated by the use of a mathematical model designed to predict the physical system under consideration. This study addresses the problem by developing a predictive model to describe permafrost thaw subsidence based upon a complete formulation of the problem. This problem is one of multiphase (air, ice, water, and solid) transport and deformation in a porous medium. The conservation of mass equations for liquid water, ice with phase change, and deforming soil solids are developed. Darcy's law is extended to include moisture movement due to thermal gradients. The quasi-static equilibrium equations and stress-strain relations that assume a perfectly elastic solid matrix are also employed. Simultaneous variations of moisture retention and phase-composition curves with temperature and pore pressure are also incorporated in the model. The energy-conservation equation, which includes terms due to viscous dissipation and compression effects, along with the other equations expressed, is found to satisfactorily represent the physical processes occurring in thawing permafrost soils. Approximations to simulate the thawing of a one-dimensional soil column are then developed from the general model.