用空气单元法求解渗流场的逸出边界问题

An air element method for overflow boundary problem in seepage analysis

依据空气单元模拟排水孔的思路,在渗流场任意可能逸出边界外布置一层渗透性较强的单元,与其他实体单元一起进行渗流计算,可以实现该边界的自动求解。与现行方法相比,不仅省去了逸出边界迭代计算的麻烦,而且避免了由于逸出点定位不准确而可能引起的渗流计算不合理或收敛困难等缺陷。算例分析表明,空气单元法的计算精度与空气单元的相对渗透系数R有关,与厚度L无关。当选取了合适的R值后,可以较好地逼近现行方法。对于因引入空气单元而造成的强弱透水介质界面处数值拟真性差的现象,还提出了加入接触面薄层单元的改进方法。方法改进后,计算精度可进一步提高。最后,以小湾水电站22#坝段渗流场计算为例,说明该法的实用性和可行性。

According to the principle of the air element method, which is used to model drainage holes in seepage analysis, a layer of air elements with higher permeability is attached to any possible overflow boundary in the seepage field, and these air elements are included along with the entity elements in a common finite element analysis of seepage, so that the overflow boundary can be automatically solved. The proposed method can not only avoid the numerical iteration in calculating the overflow boundary as in current methods, but also resolve the issues related to the inefficiency and divergence associated with the inaccurate positioning of overflow boundary. The numerical examples indicate that the calculation accuracy of the air element method is correlated with the permeability of air element but independent of its thickness. Once if the relevant parameters are well selected, the proposed method can precisely approach the current ones. Furthermore, the interface film element is introduced into the air element method in order to improve the poor imitation occurring at the contact surface between strong and weak permeable media. Finally, the application of seepage calculation in Xiaowan dam section #22 demonstrates the validity and applicability of the proposed method.