基于指数积分函数的人工冻土温度场解析研究

Study on analytical solution of temperature field of artificial frozen soil by exponent- integral function

人工冻土温度场是与空间和时间相关的且含有相变的瞬态温度场 .将指数积分函数作为人工冻土瞬态温度场的解析形式 ,通过指数积分函数的近似级数表达式和工程应用 ,说明瞬态冻土温度分布的近似解析解是可行的 ,且分别在时间和空间上服从对数规律分布 .从冻结相变过程中 ,得出了冻土帷幕扩展厚度、速度与冻结时间关系的理论表达式 ,为冻结工程分析冻土温度分布、冻结帷幕的厚度。

The temperature field of artificial frozen soil is a transient temperature field which relates to both space and time involving phase change. Regarding exponent-integral function as an analytical way of transient temperature field of artificial frozen soil, the feasibility of the analytical solution and its logarithmic distribution law on both space and time are confirmed by the approximate progressional expression of exponent-integral function and the engineering application. The theoretical function expression between the expanding depth and velocity of frozen soil wall and freezing time is acquired according to freezing procedure of phase change. Therefore, a way of analyzing the distribution of temperature, the expanding depth, the strength and the freezing time of artificial frozen soil is provided for freezing engineering.