APPLICATION OF THREE-DIMENSIONAL AND FINITE ELEMENT METHODS FOR DETERMINING THE STRESS STATE OF CYLINDRICAL TUNNEL LININGS

Authors

  • V.M. Trach (National University of Water and Environmental Engineering, Rivne)
  • A.V. Podvornyi (National University of Water and Environmental Engineering, Rivne)
  • V. I., Litnitskyi (National University of Water and Environmental Engineering, Rivne)

DOI:

https://doi.org/10.31713/budres.v0i48.30

Abstract

The proposed work presents an approach to solving an important scientific and technical problem of calculating the lining of a tunnel structure under distributed external pressure. To solve this task, relations from the three-dimensional elasticity theory for cylindrical shell structures were applied, as well as the LIRA-SAPR 2024 software package (licensed version).

The three-dimensional equilibrium equations were derived by modifying the Hu–Washizu variational principle. The dimensionality reduction of the resulting system was carried out using the analytical Bubnov–Galerkin method under specified boundary conditions at the edges and surfaces of the shell structure, by expanding the system’s stress and displacement parameters into double trigonometric series. The resulting one-dimensional system of twelfth-order ordinary differential equations was solved using the numerical method of discrete orthogonalization in the radial direction.

For solving the problem with the finite element method (FEM) using the LIRA-SAPR 2024 software package, the *Surface of rotation – Cylinder* function was applied, with element type – plates, and grid type – rectangular. The following finite elements were used: type 41 – universal rectangular shell FEM, and type 45 – universal rectangular thick shell FEM.

By applying the proposed approaches, specific parameters of the stress–strain state of a monolithic reinforced concrete shell structure, as well as of a reinforced concrete structure with an internal strengthening layer of fiber composite – boroplastic, were determined and compared.

From the analysis of the obtained results, conclusions can be drawn regarding the applicability of the outcomes obtained with the finite element approach in comparison with those derived from the spatial approach.

Author Biography

A.V. Podvornyi , (National University of Water and Environmental Engineering, Rivne)

The proposed work presents an approach to solving an important scientific and technical problem of calculating the lining of a tunnel structure under distributed external pressure. To solve this task, relations from the three-dimensional elasticity theory for cylindrical shell structures were applied, as well as the LIRA-SAPR 2024 software package (licensed version).

The three-dimensional equilibrium equations were derived by modifying the Hu–Washizu variational principle. The dimensionality reduction of the resulting system was carried out using the analytical Bubnov–Galerkin method under specified boundary conditions at the edges and surfaces of the shell structure, by expanding the system’s stress and displacement parameters into double trigonometric series. The resulting one-dimensional system of twelfth-order ordinary differential equations was solved using the numerical method of discrete orthogonalization in the radial direction.

For solving the problem with the finite element method (FEM) using the LIRA-SAPR 2024 software package, the *Surface of rotation – Cylinder* function was applied, with element type – plates, and grid type – rectangular. The following finite elements were used: type 41 – universal rectangular shell FEM, and type 45 – universal rectangular thick shell FEM.

By applying the proposed approaches, specific parameters of the stress–strain state of a monolithic reinforced concrete shell structure, as well as of a reinforced concrete structure with an internal strengthening layer of fiber composite – boroplastic, were determined and compared.

From the analysis of the obtained results, conclusions can be drawn regarding the applicability of the outcomes obtained with the finite element approach in comparison with those derived from the spatial approach.

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Published

2025-12-04

Issue

No. 48 (2025)

Section

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