中文摘要：

为确定渗流自由面,利用比例边界有限元法对二维稳定渗流场进行分析.通过比例坐标与直角坐标之间的转换,推导渗流问题的比例边界有限元方程.利用比例边界有限元空间降低一个维度,并在降维方向保持解析的特点,只对求解域边界进行离散.当比例中心选在坝体上游直线边界和坝体下面不可渗透直线边界交点时,只需离散自由面及其下游边界.并给出一种控制溢出点的控制点法.对二维坝体的稳态渗流场自由面问题进行分析并与实验结果比较.结论表明,该方法收敛快、结果较精确、数据准备工作量小.

英文摘要：

A scaled boundary finite-element method （SBFEM） is used for determining free surfaces in two-dimensional steady-slate seepage problems. Equations of SBFEM for a seepage problem are derived with a transformation from Cartesian coordinates to scaled coordinates. Go,~erning equations are discretized on boundary of computational domain by SBFEM, which reduces spatial dimension by one, and analytical procedure is applied in the reduced direction. As scaled centre is at intersection point of upstream and impermeable straight boundary of the dam bottom, only free surface and its downstream boundaries are discretized. A governing point method is used to control overflow point in the free surface. A 2-D steady seepage with a free surface in a homogeneous dam is analyzed and compared with experimental result. It shows that the method has satisfactory convergence, accuracy and less amount of data preparation.