基于复数表达的随机渗流研究

Stochastic seepage based on complex expression

以复数形式表示渗透系数,将其变异值设置为复数的虚部。利用有限单元法,通过求解复系数线性方程组计算随机渗流问题,并编制相应程序,计算结点水头和水头变异值。在应用蒙特卡罗法进行渗流计算时,仅考虑帷幕渗透系数的变异,并假设其服从均匀分布。选取水头均值与水头标准差为蒙特卡罗法渗流计算的统计特征值。从数值方面分析了基于复数表达的随机渗流计算所得的水头值及水头变异值与蒙特卡罗法计算的水头均值及标准差之间的关系,验证了所用方法在模拟随机渗流场方面的正确性和可行性。为大型复杂问题的大变异性求解提供了方便快捷的计算方法。

The permeability coefficient here is expressed in form of complex variable,the imaginary part of which is the variation value.The node head value and its variation value are calculated by self-compiling program according to the solution of linear equations with complex coefficient based on the finite element method.The permeability coefficient of curtain is considered as random variable and to be in uniform distribution by using Monte Carlo stochastic finite element method to calculate the stochastic seepage filed.The head mean value and the head standard deviation are used to represent the statistical values of the calculated results obtained by the Monte Carlo stochastic finite element method.The calculated values of head value and the head variation are compared with the head mean value and the head standard deviation by numerical simulation.The results demonstrate that the seepage calculation with permeability coefficient expressed in complex variable is correct and feasible.This study provides a convenient method for solving large complex problem under large variability conditions.