城区渗流场中建筑物间缝隙有限元简化分析方法

为解决城区渗流场中缝隙多、区域的大尺度与物体的小尺寸相差了几个数量级，有限元分析上存在的困难，根据缝隙流动的解析解，经适当地简化，将缝隙附近的渗流场分为缝外区和缝内区两部分，将缝外区流动简化为一个半径为半缝宽的井流，缝内区流动简化为一个均匀流。引入附加阻力系数，考虑缝隙出入口附近的由于过水断面突然变化而引的局部水头损失，并得到附加阻力系数的表达式。利用该式，结合渗流场中井点水头的修正公式，得到了能有效模拟渗流场中建筑物间缝隙的修正线单元公式。利用该线单元编制了相关程序模拟城区渗流场中的缝隙，使得缝隙出入口处的网格尺寸为缝隙两边的建筑物边长1/3～1/4时就能得到较为准确的结果，避免了区域性渗流场中小尺寸物体的网格划分问题，通过算例验证了该公式的精度和边界适应性。

Simplified finite element method of modeling gaps between buildings in an urban seepage field

In an urban regional seepage field, thousands of gaps between building foundations make finite element modeling and analysis very difficult, because the size of the field is larger several order than the gaps’. In order to overcome the problem, based on the analytical solution of the gap flow, the seepage field was divided into outside and inside parts. In the outside, the flow was modeled by half a well whose diameter equals the gap width. In the inside, the flow was modeled by a uniform flow. Between them a local additional hydraulic head emerged. A coefficient was deduced to take into account the local hydraulic head loss. With the coefficient and the well point hydraulic head modified method which is employed in seepage finite element analysis, a modified line element formula was gained. The formula accuracy was examined. Using the modified line element to model gaps, in neighborhood of gaps inlets or outlets, the element size can set to be one-third to one-fourth of buildings side length without losing accuracy. Examples show that modified line element can model gaps between buildings precisely and efficiently. It can greatly reduce complexity of using finite element method to model an urban regional seepage field.