The solution of Laplace equations by using the method of separation of variables in the cylindrical coordinate system is discussed. Through a series of case studies

the solution of Laplace equations is gotten and used to study the phenomenon of seepage failure and exemplify some instances. It concludes that the ununiformity of the permeability coefficients is the main reason for the seepage failure; and the seepage failure always develops along the direction of high gradient of the permeability coefficients. The authors also try to probe into the complicated mechanism of piping. This study is of great significance to some engineering problems

such as piping

flowsoil

etc.