Development of Mathematical Model of Heat and Mass Transfer in Soil, with Provision for Gradients of Soil-Water and Soil-Salt Potentials. Part 1

摘要

Frost heaving of soils has a significant influence on the stability of various buildings and constructions. It causes a rise of shallow foundation of buildings and pile of overhead pipeline, the destruction of roads and strong bends of underground pipelines on the short distance. This process is associated with the mass transfer of liquid water from thawed to frozen soil. The paper considers the problem of mathematical modeling of mass transfer in soils. The introduction of thermodynamic parameters - soil-salt potential is proved. This potential, like soil-water potential, is not constant. There is proof that the potential of all components of water-salt solution in soil may consist of the chemical potential and the potential of external volume forces, which are non-zero. The differential equation of the dynamics of pore solution was derived. This equation takes into account the gradients of potential of all components of solution, gradient of hydrostatic pressure, gravity and bulk frictional force. The paper also shown that the friction body force does not depend of type of drive force (external acceleration, the gradient of pressure or potential) at a first approximation and for small speed. Using this approach allows to describe the dynamics of the pore solution with only transmissibility coefficient.