Mathematical Modelling of the “Water — Ground Mass — Immersed Section” System

To formulate recommendations for constructing a mathematical model using the finite element method for determining the stress-strain state of immersed sections within the “water — ground mass — immersed section” system. Methods: The finite element method and the Metrogiprotrans technique were used. Results: When comparing the Metrogiprotrans technique with the finite element method for modelling the immersed tunnel sections that considers construction stages, additional force impacts from the soil foundation and the effects of sliding backfill prisms have been identified. During the mathematical modelling of the “water — ground mass — immersed section” system, an unexpected mathematical phenomenon related to hydrostatic pressure exerted from within the section has been discovered. Three potential solutions have been put forward to mitigate this effect: the introduction of a specified filling material for the sections, the application of internal “back pressure” within the section, and the substitution of the “Water Level” function with a consistent distribution of loads at each simulation stage. Following the comparative analysis of the options, the most effective solution, from a modelling perspective, that aligned with the Metrogiprotrans method, has been chosen. Practical significance: The study’s outcomes can be applied during the design phase of structures to effectively model the “water — ground mass — immersed section” system using the finite element method.