Clay core dams are widely applied in reservoir construction, regulating water resource and provide electric power. Leakage is a common problem in reservoir construction, and the leakage amount, which not only affects the economic benefits of the project, but also relates to the safety of the dam body, is difficult to estimate. According to Darcy’s law and stable seepage theory, an analytical method can be proposed to calculate the leakage of the clay core dam to gain the seepage flux in a short time. By making some reasonable assumptions, we propose formulae for seepage calculation in different conditions of the position of the groundwater levels, below or above the reservoir bottom. Both sets of formulae contain two parts of leakage calculation, i.e., leakage from the reservoir bottom and leakage from the dam body. By using the proposed analytical method, the leakage of clay core dams can be estimated considering the influence of the groundwater level. To prove the rationality of the analytical method, a simple numerical model can be established using Geo-studio 2020 to calculate the seepage flux of the clay core dam, where relative errors between numerical solutions and analytical solutions are less than 10%. To verify the feasibility in engineering applications, the proposed method was applied to calculate the seepage of a clay core dam in Sichuan, China, which was also calculated using numerical methods by establishing a three-dimensional model. The results show the rationality of the analytical method, which can strike a balance between precision and efficiency.

Back analysis for seepage parameters is a classic issue in hydraulic engineering seepage calculations. Considering the characteristics of inversion problems, including high dimensionality, numerous local optimal values, poor convergence performance, and excessive calculation time, a biological immune mechanism-based quantum particle swarm optimization (IQPSO) algorithm was proposed to solve the inversion problem. By introducing a concentration regulation strategy to improve the population diversity and a vaccination strategy to accelerate the convergence rate, the modified algorithm overcame the shortcomings of traditional PSO which can easily fall into a local optimum. Furthermore, a simple multicore parallel computation strategy was applied to reduce computation time. The effectiveness and practicability of IQPSO were evaluated by numerical experiments. In this paper, taking one concrete face rock-fill dam (CFRD) as a case, a back analysis for seepage parameters was accomplished by utilizing the proposed optimization algorithm and the steady seepage field of the dam was analysed by the finite element method (FEM). Compared with immune PSO and quantum PSO, the proposed algorithm had better global search ability, convergence performance, and calculation rate. The optimized back analysis could obtain the permeability coefficient of CFRD with high accuracy.

The calcium leaching effect inevitably increases the grout curtain hydraulic conductivity. It is diffucult to sample and obtain the leaching-related calculation parameters for deep-buried grout curtains. This study introduced the inversion method into the calcium leaching analysis to get proper leaching-related calculation parameters and accurate results. An inverse analysis model was proposed using the genetic algorithm (GA) and finite element analysis technology to solve the calcium leaching problems. The objective function is constructed using the hydraulic head and leakage quantity time-series measurements, which improves the uniqueness and reliability of the inverse results. The proposed method was applied to the inverse analysis of the hydraulic conductivity evolution of the grout curtain in a concrete dam foundation. The predicted water heads and leakage quantity are consistent with the monitored data, indicating the rationality of this simulation. The grout curtain hydraulic conductivity prediction in 100 years is also presented. The results illustrate the feasibility of the proposed method for determining leaching-related parameters and the hydraulic conductivity prediction in the leaching process.

The calcium leaching effect leads to a decrease in the impermeability of the impervious curtain. The inverse analysis strategy was introduced in this study because the calcium leaching parameters of the curtain are not easy to determine. An orthogonal design and the finite element method were used in the strategy. The time-series data of hydraulic head and leakage volume were applied to construct the objective function. The extreme learning machine (ELM) was proposed to build the reflection sets. Genetic algorithm (GA), simulated annealing (SA), sparrow search algorithm (SSA), and particle swarm optimization (PSO) were employed to accelerate the iterative search for the target parameters. The target parameters of the calcium leaching model were used for finite element verification by comparing the monitored and simulated values. The simulated values of hydraulic head and leakage by PSO show good agreement with measurements. The evolution of the curtain permeability coefficient in 100 years was analyzed. The results demonstrate the strategy’s feasibility in determining the curtain’s calcium leaching parameters and permeability coefficients.

Seepage flux is very important in many hydraulic projects such as in the upper reservoir of a pumped storage power station because of its effect on economic benefits. However, upper reservoirs with a relatively high altitude are generally located above the groundwater level; thus, their leakage is difficult to estimate accurately. Here, using steady seepage theory and Darcy’s law, we propose a simplified calculation method to estimate the leakage of slope-wall rock-fill dams with a horizontal blanket. Using a one-dimensional governing equation for unsaturated seepage flows with the assumption of porous continuous media, formulas are derived for calculating the seepage flux of the dam in a steady state with different groundwater levels, which are mainly divided into two situations: those that are lower or higher than the bottom of the horizontal blanket. Then, two engineering examples are developed to assess the proposed method; the relative errors between the analytical results and numerical results are less than 10%. The results obtained from other analytical methods introduced by other researchers are also compared with our numerical results. The comparison results show that the proposed method is reliable and can be used for the estimation of reservoir leakage in situations where rapid results are needed, such as benefit assessments and safety evaluations.