Abstract
In this paper, a mathematical model based on spherical differential unit cell is proposed as a model for studying seasonal freeze-thaw soil space infinitesimal differential unit cell. From this model, the basic equations of permafrost moisture and heat flow motion are directly derived, then the linked equations form the permafrost water-heat coupled transport model. On this basis, the one-dimensional seasonal permafrost water-heat transport equation is derived. The model reduces the original spatial three-variable coordinate system (parallel hexahedron) into a coupled equation with a single spherical radius (R) as the independent variable, so the iterations of the numerical simulation algorithm is greatly reduced and the complexity is decreased. Finally, the model is used to simulate the seasonal freeze-thaw soil in the ShiHeZi region of Xinjiang, China. The principle of the simulation is to collect the soil temperature and humidity values of the region in layers and fixed-points using a homemade freeze-thaw soil sensor, after that we solve it by numerical calculation using MATLAB. The analysis results show that the maximum relative error of the model we proposed is 4.36, the minimum error is 0.98, and the average error is 2.515. The numerical simulation results are basically consistent with the measured data, then the proposed model is consistent with the matching states of permafrost moisture content and soil temperature in the region at different times. In addition, the experiments also demonstrate the reliability and accuracy of the model.
Highlights
With regard to the recent progress on permafrost research, the results are mainly as follows: 1 During a complete annual freeze-thaw cycle, all layers of near-surface soils has generally experienced four stages: summer thawing period, spring and autumn thawing-freezing period, as well as winter freezing period
In literature [20], thermal properties of soils and various other physical properties were determined by using the heat pulse (HP) method, which was based on a linear heat source solution of radial heat flow equation, a high-pressure probe structure was proposed, the properties measured in unfrozen and frozen soils were discussed
Frozen soil was assumed to be under the conditions of the basic hypothesis specified in [24, 25], according to the principle of unsaturated soil water dynamics and related theory, based on which a seasonal frozen soil water and heat coupled migration partial differential mathematical model was built [26]
Summary
With regard to the recent progress on permafrost research, the results are mainly as follows: 1 During a complete annual freeze-thaw cycle, all layers of near-surface soils has generally experienced four stages: summer thawing period, spring and autumn thawing-freezing period, as well as winter freezing period. In literature [20], thermal properties of soils and various other physical properties were determined by using the heat pulse (HP) method, which was based on a linear heat source solution of radial heat flow equation, a high-pressure probe structure was proposed, the properties measured in unfrozen and frozen soils were discussed. Under frozen conditions, based on soil water movement and heat flow equations, this study rebuilt the moisture migration equation and heat transfer equation, frozen soil hydrothermal coupled migration partial differential equations were derived using the contact equation This model considerably simplified computational complexities, as the original three variables in three-dimensional space were reduced to only one spherical radius (R) independent variable in the coupled equations, thereby substantially reducing coupling iteration computations. Frozen soil was assumed to be under the conditions of the basic hypothesis specified in [24, 25], according to the principle of unsaturated soil water dynamics and related theory, based on which a seasonal frozen soil water and heat coupled migration partial differential mathematical model was built [26]
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