冻土水热力耦合作用的数学模型及数值模拟

将冻土体视为空间弹性体，提出了土体在冻结过程中水分场、温度场、应力场三场耦合的一般数学模型，并给出了相应的离散方程及其解法，最后给出了数值算例，并与实测值比较，证明了该模型和算法的正确性。

MATHEMATICAL MODEL FOR COUPLED MOISTURE,HEAT AND STRESS FIELD AND NUMERICAL SIMULATION OF FROZEN SOIL

The process of soil freezing is a typical problem of heat and mass transition. To simulation the processs coupling among moisture, temperature and stress fields must be considered. Assume soil is elastic body, a mathematical model is set up, the equations coupling of three fields are given below. Equation of temperature can be written as where, Equation of moisture can be expressed as and The stress-strain relation can be expressed as Think about equation (1)-(3) as well as boundary conditions, a mathematical model coupled with moisture, heat and stress fields can be constructed. To solve the problem, we use finite piement method in spatial and finite difference scheme in time domain. So the above equations can be rewritten as a matrix form Equation (4) forms the algebra equation that couples three fields. There are two kinds of coupling, one is the coupling of moisture and temperature, the other is temperature, moisture coupled with Water pressure. To solve the problem, two iterative steps must be used. After discussion, we simulate a process of soil freezing for opening water system irrigation ditch. The calculation results of water content, temperature field and stress distribution coincide with that of observation values. It demonstrates the validity and effectiveness of this mathematical model and the numerical simulation method.