中文摘要：

利用Laplace方程可以得到一类边界条件下圆柱形域内竖向分层土的水头分布问题的解，并用这些解对渗透破坏现象进行了数学描述，这些解也可应用于热传导问题。对于管涌、流土、热传导等工程问题具有一定的意义。

英文摘要：

The head distribution of vertical layered soil in the cylindrical territory, with the condition of first boundary, is mainly discussed in this article. Solutions for several problems are given by Laplace equations and used to study the phenomenon of seepage failure. These solutions can also be applied to problems of heat conduction. The study is of much significance to engineering problems such as piping, sapping, and heat conduction.