№85-16
Numerical analysis of the stress-strain state of metro tunnels under difficult conditions using Midas GTS NX
L. Shaidetska1, https://orcid.org/0000-0002-6593-0255
V. Panarin1 https://orcid.org/0009-0003-8871-9131
1National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine
Coll.res.pap.nat.min.univ. 2026, 85:198–207
Full text (PDF)
https://doi.org/10.33271/crpnmu/85.198
ABSTRACT
Purpose. Assessment and predictive analysis of the stress-strain state (SSS) of the soil mass and structural elements of the subway tunnel lining, constructed in difficult hydrogeological conditions of Kyiv (in particular, in water-saturated clay soils), to minimize operational risks and ensure the stability of underground structures.
Methodology. The calculation is carried out using numerical modeling based on the finite element method (FEM) in the Midas GTS NX software package. The study used a nonlinear elastic-plastic Mohr-Coulomb model to describe the soil behavior, taking into account the physical and mechanical characteristics of the mass. The modeling involves taking into account the staged nature of the shield tunneling, the hydrostatic pressure of pore water, and the interaction of the soil-lining system through contact elements. To eliminate edge effects, a calculation area significantly exceeding the tunnel diameter was set.
Results. The nature of the redistribution of stresses and deformations around the tunnel with a diameter of 6 m at a depth of 20 m has been established. The values of the maximum vertical displacements in the tunnel invert (heave) are +10.9 cm, while the settlement of the ground surface above the vault is recorded at 4.8 mm. The maximum total vertical stresses in the lower part of the model reach 1762 kPa. The analysis of the pore pressure showed its linear increase to 353 kN/m², while the tunnel lining acts as a waterproof barrier. Plastic zones have been determined, concentrated in the tunnel haunches and the invert, which indicates the transition of the soil to a failure state in these zones.
Scientific novelty. The dependencies between hydrogeological conditions and the nature of the formation of plastic deformation zones for shallow tunnels under the conditions of Kyiv have been established. It has been proven that in water-saturated clay masses the main deformation factor is the intensive heaving of the invert due to unloading, which prevails over surface settlement. New data have been obtained on the configuration of the plastic zones of the mass under the conditions of the simultaneous influence of the soil self-weight and hydrostatic pressure.
Practical significance. The obtained calculation data allow at the design stage to reasonably choose the reinforcement parameters of the reinforced concrete lining and make decisions on the need for additional strengthening of the surrounding soil mass. This allows to significantly reduce the risks of flooding and uneven deformations of tunnels, ensuring reliable functioning of the city's transport infrastructure under conditions of increasing loads.
Keywords: subway tunnel, stress-strain state, numerical modeling, finite element method, Midas GTS NX, Mohr-Coulomb model, settlement trough, geomechanical safety.
References
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date of first submission of the article to the publication – 04/10/2026
date of acceptance of the article for publication after review – 05/11/2026
date of publication – 06/30/2026