Numerical Analysis of the Optimized Cross-Section of Roller-Compacted Concrete Dams Using the Finite Element Method

Background and Objectives
People construct dams for various purposes, such as flood control, hydropower generation, and managing water for drinking and agriculture. One of the most effective ways to manage water is by using dams. However, constructing dams has some financial changes, and decreasing these costs helps governments diminish their financial issues. So, by combining the principles of engineering and economics, engineers can design structures at low cost. Nowadays, the stability of structures is not sufficient, and engineers have to design buildings with sufficient strength to withstand various loads and be economically optimal. Roller-compacted concrete (RCC) is used in hydraulic structures due to its higher strength and high execution speed. The history of using roller-compacted concrete versus conventional concrete shows that the cost per cubic meter of roller-compacted concrete is far less, with an average cost reduction ranging from 25 to 50%. This reduction in costs is due to the materials used, the amount of cement used, and the ease and simplicity of the implementation method. More studies focused on the mechanical behavior of roller-compacted concrete dams, such as thermal performance and seismic performance. However, there were not sufficient studies regarding the performance of these dams by reducing their volume in various geometric shapes. So, studies on the maximum amount of volume reduction possible for dams without reducing mechanical properties are essential.

Methodology
The study employed the finite element method (FEM) using ABAQUS software to model and analyze various cross-sectional designs of RCC dams. This software could simulate different structures under various loads, so it could solve complicated problems using static, dynamic, thermal, and large deformation analysis. In the finite element method for solving problems, the structures are divided into smaller components that are called elements. By increasing the number of elements, the accuracy of the model increases as well. Increasing the number of elements beyond a certain limit will not only increase the computational cost but also will not result in a significant improvement in the accuracy of the solution. In this project, for the concrete section that was modeled as a solid volume, the node spacing was set to 0.01 mm, which resulted in 20,850 eight-node 3D elements of type C3D8R. For the soil part that was modeled as a solid volume, the node spacing was set to 0.02 mm, which resulted in 15,375 eight-node 3D elements of type C3D8R. For validation of the simulation process, the article by Zhang et al. (2019) was selected as a reference and evaluation.

Findings
First of all, a topology optimization tool in Abaqus software was used for volumetric optimization (20% volume reduction without reducing resistance). Then, based on considering the result of optimization, models with ideal and practical geometries were designed in terms of implementation. After, selecting the appropriate meshing method for the model and other required parameters, the numerical model of the structure examined in this study (which was derived from the study by Zhang et al.) was created and the desired simulations were performed. For validation, the obtained results for the displacement of the dam crest in the horizontal and vertical directions were compared with the results obtained from the study of Zhang et al. The horizontal and vertical displacements of the dam crest were obtained to be 18.648 and 17.20, respectively, which had a maximum error of 1.3% and 1.23% compared to the prior study. Which indicated the accuracy of the selected methods and the materials applied in the simulations performed. For the optimization analysis, the volume parameter was considered as the objective function and the strain energy parameter as the control function. After performing optimization analysis and reducing the model volume by approximately 30% by the software, under the same loading conditions, the maximum stress value decreased by 34.5% and the maximum displacement of the dam crest in the vertical direction decreased. While the maximum displacement of the dam crest in the vertical direction doubled, it should be noted that due to the lack of increase in the stresses generated in the dam, this increase in displacement was due to the increase in the flexibility of the dam against the applied forces and did not indicate a decrease in the dam's resistance. Based on the optimization results, several models were designed for the application of construction conditions and structural aesthetics of the dam by Abaqus software. The model that had columns with non-sloping side walls and simple shapes, making it easy to use and can be displayed with long and short spans between the columns, was the best-designed one. The volume of this model was 5905911 cubic meters, which was an approximate reduction of 30.61 percent compared to the initial volume of the dam used in the Zhang et al. paper.

Conclusion
This paper demonstrated the optimization of RCC dams through geometric refinement. By using finite element method analysis by Abaqus software, engineers can design more efficient and cost-effective dam structures. The findings supported the reduction of almost 30% of concrete volume without decreasing the strength of the dam. The study’s outcomes suggested that a well-designed RCC dam had columns with non-sloping side walls and simple shapes, making it easy to use and display with long and short spans between the columns. This choice was based on the largest amount of reduction in dam volume compared to the initial volume.