摘要
Signorini型变分不等式在求解有出渗点的渗流自由面问题时,消除了出渗点的奇性,克服了网格的依赖性。在迭代求解过程中多采用约束迭代法,这种数学约束比较严格,对于自由面穿过的单元计算不容易收敛,会造成结果在两种解中震荡。笔者在变分不等式的基础上修改了迭代公式,对数学约束进行了修改,建立了变带宽的迭代方法。通过修改迭代算法提高了Signorini型变分不等式方法的数值稳定性,同时减少了迭代时间。地下厂房开挖后地下水会从洞室的边墙渗出,临界出渗点的确定对分析渗漏量和排水孔效果起到关键作用。通过对工程中开挖边界和排水孔边界的渗流计算模拟分析,证明了改进迭代算法后的Signorini型变分不等式在复杂非线性强的三维渗流计算中收敛性较好。
Signorini-type variational inequality has the advantage to eliminate the singularity of the infiltration point and to overcome the mesh dependency when solving the seepage free surface problem. Constraint iteration method is used in the iterative process, and the mathematical constraint is more stringent. For the free surface through the unit calculation, it is not easy to converge and even results in a shock between two kinds of solutions. On the basis of the variational inequality, the authors modify the iterative formula. The mathematical constraints are revised, and an iterative method with variable bandwidth is developed. Modifying the iterative algorithm improves the numerical stability of the variational inequality formulation of Signorini, and reduces the iteration time. After the excavation of underground powerhouse, the groundwater normally leaks from the side wall of the cavern, the determination of critical percolation point plays a key role in the analysis of leakage and the effect of drainage hole. The modified Signorini-type variational inequality is applied to simulate the seepage flow in the excavation boundary and the drainage hole of a typical project, which proves that the modified method has better convergence in the complex nonlinear three-dimensional seepage calculation.
作者
邓高阳
肖明
陈俊涛
DENG Gao-yang XIAO Ming CHEN Jun-tao(State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, Hubei 430072, Chin)
出处
《岩土力学》
EI
CAS
CSCD
北大核心
2017年第3期762-768,共7页
Rock and Soil Mechanics
关键词
变分不等式
变带宽迭代
出渗
边界条件
variational inequality
variable bandwidth iteration
outlet seepage
boundary condition
