Yuelu Zhu

To address the issue of heat release during the construction of concrete dams, this study employs the approach of embedding water pipes for temperature control. Taking a large-volume concrete gravity dam in China as an example, considering environmental and river water temperatures, inputting concrete thermodynamic parameters, and taking various factors such as pipe layout, calculation parameters, pipe radius, material, spacing, and water temperature into account, the study utilizes finite element software for simulation modeling. It systematically discusses the relationship between cooling effects, costs, and engineering safety. The research results indicate that, under the condition of a rectangular section layout, with a pipe radius of 0.01 m and a spacing of 1.5 × 1.5 m, the comprehensive effect is optimal. The influence of different pipe materials on temperature reduction is minimal. When changing pipe materials, only material costs and their impact on structural safety and durability need consideration. Additionally, excessively low water temperatures during water passage can lead to internal concrete cracking, requiring attention during construction.

The classical Richards Equation of water infiltration in unsaturated soil is a partial differential equation, which is nonlinear and difficult to obtain analytical solution. Taking time as the least action variable, the infiltration path as a functional of time is established based on Richards Equation. The vertical infiltration problem of unsaturated soil under gravity is transformed into the functional extremum problem, and solved by Euler-Lagrange Equation. The results show that the diffusion coefficient D(θ) has a function relationship with the depth of wetting front. When the type of diffusion coefficient is known, the moisture content of wetting front at specified depth, the moisture content of the farthest wetting front and the maximum entropy distribution of soil moisture content can be obtained at the optimal path. Taking the optimal path as the standard, the accuracy of solving Richards Equation by Boltzmann transformation and linear transformation is tested.