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In this paper, we develop a numerical solution to equations derived in the first part of this study to simulate the thaw subsidence of an unsaturated frozen soil due to surface heating. Solutions obtained in terms of pore pressure, temperature, degree of unfrozen water content, ice content, and porosity provide the spatial and temporal variations of these quantities in a thawing soil column. A one-dimensional form of governing equations is discretized by employing a Crank-Nicolson finite-difference scheme. These highly nonlinear equations are then solved by an iterative procedure at every time step for predescribed positive surface temperatures that produce thawing. The numerical solutions are obtained for a 1-m silt column. Results show that, above the frozen region, unfrozen water saturation increases due to low hydraulic conductivity, which prevents the melting ice from draining, thus causing accumulation of water above it. It has also been observed that most of the settlement at the surface is due to thaw consolidation rather than settlement due to drainage. The former is completed in seven days of a 12-day simulation period. Furthermore, a sensitivity analysis was carried out to determine the response of the simulation to deviations in the values of certain parameters. It is found that the settlement estimations are very sensitive to the thaw-settlement parameter and phase-composition curve, thus requiring accurate determination of these parameters for a reliable simulation of the thaw-consolidation process.

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.

A dynamic subtime-stepping method is described for solving contaminant transport problems that utilize higher-order implicit time-marching procedures with higher-accuracy nonoscillating spatial-discretization methods to resolve sharp-plume fronts in advection-dominated systems. Nonoscillating spatial-discretization methods for the advective term prevent unphysical oscillations and minimize numerical diffusion. Second-order temporal accuracy is achieved by using the Crank-Nicholson implicit scheme, however nonoscillating properties may be violated for Courant Numbers larger than one, leading to spurious oscillations. The proposed subtiming method allows use of small time-step sizes in critical portions of a domain, with larger time-step sizes in other locations. This locally limits the Courant number where required and still keeps the general solution free of time-step size restrictions. This technique makes it possible to apply higher-order nonoscillating schemes with higher-order temporal weighting for advection-dominated flows, even when the Courant number is much greater than one. Feasibility and applicability of the dynamic implicit subtiming method are demonstrated through three proof-of-concept example problems. [ABSTRACT FROM AUTHOR]