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Article information
2014 , Volume 19, ¹ 4, p.19-31
Vabishchevich P.N., Vasilyeva M.V., Gornov V., Pavlova N.V.
Mathematical modeling of the artificial freezing of soils
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 °C to +35 °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 is given for the two-dimensional problem depending on the time step and the phase transition width. 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 calculations were performed on a computational cluster of NEFU. The graphs illustrate the effectiveness of the use of freezing columns for sustainability the foundations of buildings and structures. Aknowlegements: This work was supported by RFBR grants 12-01-98514 and 13-01-00719A. Received 6 November 2013.
[full text]
Keywords: Numerical modeling, artificial freezing, heat transfer, phase transition, Stefan problem, finite element method, the computing cluster
Author(s):
Vabishchevich Petr Nikolaevich
Dr. , Professor
Position: Head of Laboratory
Office: Nuclear Safety Institute, Russian Academy of Sciences, Head of the Laboratory
Address: 115191, Russia, Moscow, 52, BolshayaTulskaya
Phone Office: (495) 955-24-21
E-mail: vab@ibrae.ac.ru
SPIN-code: 6741-6981Vasilyeva Mariya Vasiljevna
PhD.
Position: Head of department
Office: North-Eastern Federal University, Institute of Mathematics and Informatics
Address: 677891, Russia, Yakutsk, Belinskogo str., 58
Phone Office: (924) 660-52-63
E-mail: vasilyevadotmdotv@gmail.com
Gornov Victor
Position: Director
Office: JSC "Insolar-Invest"
Address: 121433, Russia, Moscow, Belinskogo str., 58
Phone Office: (499) 144-01-75
E-mail: insolar-invest@yandex.ru
SPIN-code: 7269-5312Pavlova Natalya Vasiljevna
Position: Senior Fellow
Office: North-Eastern Federal University, Institute of Mathematics and Informatics
Address: 677891, Russia, Yakutsk, Belinskogo str., 58
Phone Office: (924) 661-75-57
E-mail: npav@rambler.ru
SPIN-code: 6249-0580 References:
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Bibliography link:
Vabishchevich P.N., Vasilyeva M.V., Gornov V., Pavlova N.V. Mathematical modeling of the artificial freezing of soils // Computational technologies. 2014. V. 19. ¹ 4. P. 19-31
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