利用温度场计算渗透流速的数学模型

通过温度场探测堤坝渗漏的技术已经得到了广泛应用,利用温度场求解相关渗流参数的理论也得到快速发展。利用温度场计算渗流参数时通常假定存在一条或多条集中的渗漏通道,并在此基础上建立数学模型,计算渗漏通道的渗透流速及渗漏流量,但这种处理方式仅对渗漏通道进行研究,得到的近似结果并不一定符合工程实际。部分学者利用热传导理论及渗流理论建立数学模型,但由于其边界条件假定过于理想,模型在应用过程中存在局限性。在总结前人研究成果的基础上,设定了更符合实际情况的边界条件,建立有限空间内基于渗流问题的二维温度场数学模型,并在一定初始条件和边界条件下解出模型的解析解,最后以西藏某水库为例,验证了该数学模型的合理性。

A mathematical model for calculating penetration velocity using temperature field

Detecting dam leakage through the temperature field has a wide range of applications to practical works, and the theory using temperature field to solve seepage parameters is also developed rapidly. Scholars use temperature field to calculate seepage parameters. They assume that there are one or more leakage passages to establish a mathematical model which is used to calculate seepage velocity and seepage discharge. But this approach is only for dealing with problems of leakage channel, and this computation can’t be applied to all projects. Some of the scholars have established the mathematical models by using heat transport theory and percolation theory. However, those models are difficult to apply to solving all practical problems in engineering works because their boundary conditions are too ideal. Based on the summarization of previous findings, we have established a two-dimensional temperature model of the dam in semi-infinite space, and obtained the analytical expressions of the temperature in the initial boundary conditions in this study. At last, taking a reservoir project in Tibet as an example, the rationality of the application of this model to practical works is verified.