# A Comprehensive Safety Analysis Study for Concrete Core Dams
## 1 Introduction  
In recent decades, many problems have arisen with dams due to their age and the use of outdated technology [1, 2]. Many dams have fallen into disrepair and, as a result, have faced serious safety problems. Due to a lack of consideration of soil material specificity, earth-rock dams constructed with a low-technology approach have suffered from varying degrees of leakage, cracking, and so on. In order to allow such dangerous earth-rock dams to continue in operation, reinforcement measures are badly needed to restore dam body safety. Therefore, the analysis of reinforcement materials has become an important aspect of the reinforcement process. Concrete, which is widely used in all kinds of structures for its unique material character, was finally selected as a cheap reinforcement material. However, there has been little reinforcement analysis of the clay core with its low-elastic-modulus material [3, 4, 5]. With conventional concrete, the elastic modulus of the anti-seepage wall is higher under water loading. Large deformations and stress concentrations will occur. Cracks may be generated in the wall by tensile stress, thereby affecting the seepage effect. The importance of a low-elastic-modulus material for such a concrete reinforcement dam project is considered here. Furthermore, by considering different values of the elastic modulus for the anti-seepage wall of a practical project, the effect of low elastic modulus on the anti-seepage wall is studied [6, 7, 8]. Recently, 3D seepage numerical analyses have been performed, and hydraulic coupling analysis is used for the seepage stability of thedam [9; 10]. In addition, it is necessary to consider related research into a number of reinforcement projects concerned with dangerous dams [11; 12; 13; 14]. The research methods for the seepage calculation and analysis of an earth-rock dam mainly include: theoretical solution, physical simulation, and numerical simulation. Among them, the finite element method is one of the most widely used. The finite element method can be used to solve stable seepage and unstable seepage, and the two-dimensional and three-dimensional models can be processed. It can not only face the heterogeneity of the embankment foundation but also conduct research on the anisotropy. Therefore, the existing seepage calculation theory can basically meet the seepage analysis needs of similar embankment projects [15]. For seepage analysis in the case of free surface, it is mainly about the calculation method of the invariant grid, that is, it is studied in the fixed grid. The representative methods are virtual element method, the improved method proposed for three-dimensional problems, nonlinear stress analysis based on the residual flow method with the concept of initial stress, and the proposed initial flow method [16]; [PERSON] proposed the Galerkin method for fixed grid research, and [PERSON] proposed the residual flow method [10; 17]. The commonly used fixed grid methods mainly include: virtual element method, initial flow method, grid correction method, element permeability matrix adjustment method, residual flow method, node virtual flow method, etc. The virtual element method is to calculate the intersection point between the free surface and the element boundary line through the node head value obtained in the last calculation and then move some nodes of the element across the free surface to make them fall at the intersection point [18]. The free surface divides the element into a real seepage area and a virtual area. The virtual area of seepage will not be involved in the next finite element calculation, and the calculation area of seepage will continue to approach the real area of seepage, and the result will also approach the true solution. When moving some nodes of the element across the free surface, the elements above the free surface do not participate in forming the penetration matrix. During the iteration process, as the free surface moves up, the iteration cannot continue.