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Mathematical modeling of the artificial freezing of soils. (Russian. English summary) Zbl 1382.74128

Summary: Research of changes of soil temperature regime is necessary for the geotechnical studies of the construction objects in regions where permafrost soils are presented. During seasonal thawing of frozen soil, their physico-mechanical characteristics are changed, which leads to the violation of their bearing capacity. Artificial freezing of soils using cooling devices is applied near the piles for sustainability foundations of buildings and structures. It was done by creating a large mass or piles of frozen ground around boulders, which prevents the soil from thawing during the summer period.{ }For numerical simulation of the process, we design the mathematical model of heat and mass transfer that takes into account the freezing temperature of the liquid in the seasonal cooling devices and typical outside temperature for Yakutia (from \(-55\;^\circ\mathrm{C}\) to \(+35\;^\circ\mathrm{C}\)). Mathematical model of the process is described by nonstationary heat equation with phase transitions of pore water. The numerical implementation of the problem is based on the finite element method using FEniCS library of scientific computing. Comparison of the temperature isotherms and error dynamics at different computational grids depending on the time step and the phase transition width is given for the two-dimensional problem.{ }Results of numerical simulation of the three-dimensional temperature fields after five years (spring, summer, autumn, winter) are given in the presence of 39 freezing columns. The simulations were performed on a cluster computer system at North-Eastern Federal University, Russia. The obtained results are showing the good effect of using the freezing columns for improving the sustainability of the foundations of buildings and structures.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74L10 Soil and rock mechanics
80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
80A20 Heat and mass transfer, heat flow (MSC2010)
80A22 Stefan problems, phase changes, etc.

Software:

FEniCS; SyFi
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