无单元Galerkin法的电流场与渗流场耦合正演

Coupled forward of seepage field and current fields based on the element-free Galerkin method

联合求解渗流场与电流场是确定土石坝渗流精确分布及评价渗流严重程度的重要途径.为解决水文-地球物理方法中存在的渗-电拟合度差及分辨率损失严重等问题,针对电性参数对水文状态变量的敏感性,本文开发一种基于无单元Galerkin法(Element-Free Galerkin Method,EFGM)的渗流场与电流场耦合正演算法.一方面,通过引入岩石物理关系经验公式及水文状态变量构建耦合模型;另一方面,通过滑动最小二乘法构造形函数,利用罚函数计算边界条件,以解决耦合模型的构建过程中对网格单元过度依赖问题来提高渗-电拟合精度.数值模拟的渗-电关联响应及耦合正演中,分析了土石坝内电流场及渗流路径,探索了各分量对土石坝不同附属结构体的异常响应特征.关联响应结果显示,饱和区内渗-电关联响应吻合较好.但由于非饱和渗流的特殊性,非饱和区介质岩石的物理特性会随着饱和度、孔隙度等因素的变化而发生改变,从而导致土石坝内非饱和区物性参数的分布与饱和区不同,从而造成非饱和区内渗-电场关联响应存在差异.在非饱和区域,耦合电位及电流密度分布与渗流分布吻合度高.渗-电耦合结果对实施模型约束的水文-地球物理耦合反演具有重要理论和实际意义.

Jointly solving the seepage and current fields is essential for determining the precise distribution of seepage in earth-rock dams and assessing its severity.In an effort to tackle the issues of insufficient fitting of seepage-electric relation and resolution loss in the hydrological-geophysical method,this paper addresses the sensitivity of electrical parameters to hydrological state variables and develops the coupled seepage-current forward modeling based on the Element-Free Galerkin Method(EFGM).On the one hand,the coupled model is constructed using the empirical formula for rock-physical relationships and the results of hydrological state variables;on the other hand,the sliding least squares method is employed to construct the shape function,and the penalty function is used to calculate the boundary conditions to solve the of over-dependence problem on grids in the coupled model construction and improve the seepage-electric fitting accuracy.The correlation response of the seepage field and current field was conducted separately through numerical simulations,the analysis focused on the current field and seepage path in the earth-rock dam,and compared the anomalous response characteristics of each component to the different accessory structural bodies of the earth-rock dam.The correlation response results indicate that the correlation response of seepage and electric field in the saturated zone is in good agreement.Whereas,due to the specificity of unsaturated seepage,the petrophysical properties of an unsaturated zone vary with saturation,porosity and other factors.It consequently led to a different distribution of physical parameters in the unsaturated zone from that in the saturated zone,causing differences in the correlation response of seepage and current field in the unsaturated zone.The coupling potential and current density distribution in the unsaturated zone are in good agreement with the seepage distribution.The results of the coupled seepage-current fields are considered significant in both theoretical and practical terms for constructing a hydrological-geophysical coupling inversion using model constraints.