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Searching for the precise solution of the free surface has remained the main bottleneck in analyzing the unconfined seepage problem for earth-rock dams. This paper proposes an approach to solve classic earth-rock dams using the smoothed finite element method (S-FEM). To overcome the problems of complex calculation and accuracy loss caused by integrating the area of intersecting elements in saturated seepage, this paper optimizes the shape function calculation by reducing the area integral to a line integral along the elements. To achieve a balance between efficiency and accuracy, we investigated the distinct effects of various smooth elements on computational efficiency, which included computation time and iteration times. Moreover, we first explored the extensive effect of seepage anomalies and their positional changes on hydrological state variables, including head, free surface, overflow point, seepage velocity, and fluid pressure. This exploration presented could provide a potential for developing multi-parameter seepage inversion and serve as constraints for hydro-geophysical inversion. [ABSTRACT FROM AUTHOR]

Seepage analysis is the central issue in solving the unconfined seepage problems from complex earth‐rock dams. The precision and efficiency of seepage simulation are the major technical barriers to exploring the heterogeneities of hydrological state variables in dams. This paper addresses the heterogeneity of the saturated‐unsaturated zones of dams and develops the smoothed finite element method (S‐FEM) capable of solving the seepage problem in domains with arbitrary geometry and continuously varied permeability. The gradient smoothing technique, in which the area integrals are transformed into the line integrals around edges of smoothing cells, is used to obtain the element matrices, which is used to simplify the solution of seepage problem. To be specific, we employ Van Genuchten method to modify the hydraulic conductivity of unsaturated zones medium and Signorini condition to convert the outflow boundary into the water head boundaries. The precision of the proposed method together with the importance of considering the unsaturated zones are first deliberated by the verification tests. Then, to quantify the impacts on the hydrological state variables, we focus on the heterogeneity of the entire zones through exploratory tests. The results show that the presence of leakage anomalies and auxiliary dam structures has a significant effect on the redistribution of hydrological state variables, which convinces that the findings may lay the foundation for the development of multi‐parameter seepage inversion and the derivation of coupled hydro‐geophysical inversion using the most appropriate starting model. [ABSTRACT FROM AUTHOR]

The critical challenge facing the modeling accuracy of borehole-to-surface electrical potential (BSEP) is the singularity effect resulted from the field source and the truncation error due to improper boundary conditions. However, different boundary conditions can reduce the truncation error by enlarging the computational domain. This enlargement undoubtedly causes a significant increase in the calculation burden. To some extent, the mixed boundary condition-based finite element method (MBC-FEM) can mitigate this problem. However, it is inapplicable to the BSEP modeling with line source because these algorithms were initially derived from the point source. For improving the BSEP modeling efficiency and precisely represent the specific correlation between BSEP observation results and the spatial location of the abnormal underground body, this paper introduces a novel finite-infinite coupling method (FICM) based on the secondary potential of arbitrary line source for three-dimensional BSEP modeling. By employing the variational principle and the different interpolation shape functions of both the FEM and the infinite element method (IEM), we discretize the function of three-dimensional line field source in the elements. The proposed coupled algorithm is then tested on a uniform half-space model, a low-resistance spherical anomaly model and an international standard model. The results show the proposed FICM can eliminate the singularity effect to reduce the truncation error. More importantly, the calculation efficiency is significantly improved by essential virtue of the needlessness of enlarging the computational domain, as well as the one-off generation of coefficient matrices. In this sense, the proposed FICM represents a more appropriate candidate for BSEP forward and inversion when a large-scale calculation is involved, especially in terms of irregular underground abnormal bodies in the line source conditions. • Field-source singularity effect is eliminated by quadratic field and infinite element. • Modeling efficiency can be improved by one-off generating the coefficient matrices. • Increasing the calculation speed of BSEP modeling by more than 50%. [ABSTRACT FROM AUTHOR]