摘要
Bathe算法将浸润面确定问题转变为常规的非线性本构问题,Signorini条件将出溢面边界转化为常规的水头边界进行处理。由于非饱和渗流问题本身就是一个非线性渗透本构问题,将上述2种方法的联合使用,避免变分不等式的求解,在常规非线性有限元求解框架内做最小程度的改动基础上,实现饱和–非饱和渗流的求解,着重探讨以下几个问题:(1)Bathe方法收敛性的改善及其修正系数的三维推广;(2)适用渗流问题的Signorini条件边界交换算法及其实现;(3)提高非饱和非稳定渗流问题求解收敛性及质量守恒性的欠松弛处理方法。最后,通过典型的算例,讨论上述算法应用中的一些问题及其适用性和精度。
Bathe algorithm converts the locating of the phreatic surface to a nonlinear constitutive problem. And the implication of Signorini condition can simulate a seepage face as a head-fixed boundary through iterative calculation. Because an unsaturated seepage problem is also a nonlinear flow problem, the implication of Bathe algorithm and Signorini condition makes it possible to model both saturated and unsaturated seepage problems with a unified method by a minimal modification to an ordinary finite element method, and avoiding solving a variational inequality system. The followings are discussed mainly： （1） the improvements of Bathe algorithm in converge and its generalized form in a three-dimensional model; （2） the implement of the switching algorithm of Signorini condition to solving seepage problems; and （3） the under-relaxation scheme to improve the mass conservation and converge properties when an unsteady unsaturated problem is solved. Finally, some numerical examples are solved to evaluate the applicability of the proposed method; and the results are compared with those available in the literature.
出处
《岩石力学与工程学报》
EI
CAS
CSCD
北大核心
2013年第11期2275-2282,共8页
Chinese Journal of Rock Mechanics and Engineering
