三维非稳定渗流自由面边界积分项的精确数值计算

利用固定网格法分析三维非稳定渗流问题时,将要面对两项积分难题:以自由面及单元表面为边界的空间积分及以自由面为边界的曲面积分。针对常用的任意8结点6平面三维普通单元,提出采用坐标变换及等参变换技术求取空间积分项的精确数值解;至于曲面积分项,建议改用单元非饱和区部分表面作为积分边界,经过坐标变换及等参变换处理积分边界后,利用高斯数值积分可求出曲面积分项的精确数值解。通过一个普通单元及一项均质半无限边界堤坝的实例分析,表明此方法的精确性和稳定性良好。

Exact numerical integrals on free surface boundary of 3D unsteady seepage problem

When using the fixed mesh method in analysis of 3D unsteady seepage problem, one will face 2 difficult integral problems:the spacial integral with free surface and the element surface as the boundary and the curve surface integral with free surface as the boundary.Against the common and randomly used three-dimensional 8-nodes 6-planes ordinary element, it is proposed that an exact numerical solution of space integral can be obtained by using the technology of coordinate and isoparametric transformations.With regard to the curve surface integral, it suggested to switch using that part of element surface in unsaturated zone as the integral boundary, and then through working for the integral boundary with the coordinate and isoparametric transformations, an exact numerical solution to the curve surface integral can be obtained by using Gaussian numerical integration.The analysis of a common element and a practical example of a dam under a homogeneous semi-infinite boundary can illustrate a rather good accuracy and stability of this method.