基于无单元Galerkin法的饱和—非饱和土石坝渗流正演模拟

Simulation of seepage in saturated-unsaturated earth-rock dam based on element-free Galerkin method

在土石坝渗流正演模拟中,仅研究饱和区域的渗流场并不能全面真实地反映出土石坝地下渗流状态,非饱和渗流区域的研究同样至关重要,利用无单元Galerkin法对饱和-非饱和渗流域进行求解。首先从达西定律出发,推导了渗流方程及边界条件,其中详细推导了无单元Galerkin法——通过滑动最小二乘法构造形函数,同时利用罚函数的方法计算边界条件。然后,通过与GeoStudio软件计算出的仅饱和渗流场以及饱和-非饱和渗流场进行比较,证明了该方法的准确性及有效性。最后,通过不同的均质和非均质模型,研究了坝体中零压力线、水头值、孔隙压力、含水率的分布。无单元Galerkin法只需要通过节点来实现对全域渗流场的精确逼近,解决了对网格单元的依赖问题,与其他数值方法相比,其具有前期处理数据简单和精度高的优点,更适合稳定饱和-非饱和渗流场这种复杂情况的正演模拟。

In the seepage forward modeling of earth-rock dams,the study of seepage field in saturated area alone can not fully reflect the underground seepage state of earth-rock dams,the unsaturated seepage field is just as important.Here,the saturated-unsaturated seepage field is solved by the element-free Galerkin method.Firstly,the seepage equation and boundary conditions are derived from Darcy’s law,and the element-free Galerkin method is derived in detail.The essence of Galerkin method is to construct a form function by moving least squares method,and to calculate the boundary conditions by penalty function.Then,the accuracy and effectiveness of the method are proved by comparing the results of the saturated seepage field and the saturated-unsaturated seepage field calculated by GeoStudio.Finally,the distribution of zero pressure line,water head value,pore pressure and water content in the dam body is studied by different homogeneous and heterogeneous models.The element-free Galerkin method only requires nodes to achieve accurate approximation of the whole domain seepage field,which eliminates the dependence on grid cells.Compared with other numerical methods,this method has the advantages of simple early processing data and high precision,so it is more suitable for the complex forward simulation of the stable saturated-unsaturated seepage field.