含排水孔渗流场的p型自适应复合单元法分析

SEEPAGE ANALYSIS CONSIDERING DRAINAGE HOLES BY p-VERSION ADAPTIVE COMPOSITE ELEMENT METHOD

用复合单元法进行渗流分析时,视排水孔为强渗透介质,并将其作为“空气子单元”置于常规岩(土)体单元内部,形成涵盖排水孔的复合单元。复合单元法的计算网格可以较为“粗糙和随意”。但由于在排水孔附近流场变化剧烈,常规的低阶形函数已不能满足精度要求。采用p型自适应技术提高复合单元的形函数阶次后,就能够较好地模拟排水孔附近处的渗流场。应用p型自适应复合单元法,可以将复杂的前处理问题转化为复杂的计算问题,从而极大地降低了对网格剖分的要求,当排水孔的位置发生变化时,也无需改变计算网格。算例分析表明该方法的优越性。

Abstract. In seepage analysis using the composite element method（CEM）, the drainage holes are regarded as a kind of material with high permeability coefficient and are treated as ＂air sub-elements＂ contained in the conventional rock（soil） element, which is called ＂composite element＂ . By CEM, the drainage holes need not be meshed out and the mesh can be ＂coarse and random＂, which makes the mesh generation work relatively convenient. As the conventional shape function of lower order is not accurate enough to simulate the strongly nonlinear flow field around drainage holes, the p-version adaptive algorithm is implemented in the CEM to get a better solution of the seepage field around the drainage holes. The p-version adaptive CEM can convert the complicated preprocess problem into a complicated computation problem. In this way, the mesh generation becomes less restricted; calculation mesh need not be regenerated when the design scheme of drainage holes is changed. Numerical example shows the advantages of the new CEM.