The method for calculating filtration under dams with homogeneous curvilinear anisotropy of the soil
Nikolay P. Petrov - Cand. Sc. (Physics and Mathematics), Associate Prof., Associate Prof. of Chess and Computer Mathematics Dept. Ural State University of Economics
Svetlana N. Petrova - Cand. Sc. (Pedagogy), Associate Prof., Associate Prof. of Humanities and Natural Sciences Dept. UMMC Technical University, Associate Prof. of Chess and Computer Mathematics Dept. Ural State University of Economics
Natalia V. Korzhavina - Cand. Sc. (Pedagogy), Associate Prof., Associate Prof. of Humanities and Natural Sciences Dept. UMMC Technical University, Associate Prof. of Transport and Energy Systems Dept. Cheboksary Institute (branch) of Moscow Polytechnic University
Abstract
Contemporary problems in the dam construction under difficult geological conditions form key challenges for hydrogeology, ranging from the stability of structures to environmental concerns. The article deals with the development of a method for calculating filtration under dams, taking into account the homogeneous curvilinear anisotropy of the soil. The main theoretical methods for calculating filtration rely on simplified assumptions (mathematical and physical models) such as the soil isotropy and the linearity of the shape of structures. The study shows that such basic assumptions may lead to significant errors in theoretical calculations, especially in real conditions with anisotropic soil properties and the curvilinear geometry of dams. It creates a need to develop new approaches that take into account all of these factors. The paper presents the results of theoretical studies on filtration flows under dams, which include anisotropic properties of soils, and demonstrates the practical application of these studies to specific types of hydraulic structures and to the soil anisotropy.
Keywords: filtration; stream function; velocity potential; dam; anisotropy.
For citation: Petrov N. P., Petrova S. N., Korzhavina N. V. The method for calculating filtration under dams with homogeneous curvilinear anisotropy of the soil. Digital Models and Solutions. 2025. Vol. 4, no. 4, pp. 49–58. DOI: 10.29141/2949-477X-2025-4-4-4. EDN: UVUZDI.
