An approximate solution that can predict phreatic line through similarity transformation by directly using second-order nonlinear partial differential equations, which is used for one-dimensional unsteady seepage flow analysis is proposed. The proposed approximate solution, derived using similarity transformation, confirms the change of the phreatic line over time in the earthen dam. To evaluate the applicability of the approximate solution, the prediction of the phreatic line using similarity transformation is then compared with that of conventional methods by Kozney, Casagrande, and Schaffernak-Iterson, as well as with numerical and experimental test results. It is noted that the approximate solution can predict the phreatic line reasonably well in homogeneous earthen dams.

提出了一种直接利用二阶非线性偏微分方程通过相似变换预测潜水线的近似解，用于一维非定常渗流分析。所提出的近似解是使用相似变换得出的，证实了土坝中潜水线随时间的变化。为了评估近似解的适用性，然后将使用相似变换的潜水线预测与 Kozney、Casagrande 和 Schaffernak-Iterson 的传统方法以及数值和实验测试结果进行比较。值得注意的是，近似解可以很好地预测均质土坝中的潜水线。