Tula State University (Tula, Russia)

A. S. Sammal, Doctor of Engineering Sciences, Professor, assammal@mail.ru
S. S. Yudin, Post-Graduate
I. Yu. Voronina, Candidate of Engineering Sciences, Associate Professor

The authors propose a new analytical method of multi-layered lining design for tunnels constructed at interfaces of rocks with different characteristics of deformation under the influence of the main static loads—gravitational forces, external pressure of groundwater and pore water pressure (for hydraulic tunnels of outlet works). The method involves rigorous solutions of contact problems in elasticity for a piecewise-homogenous medium composed of two semi-infinite heterogeneous domains that model overlying (top) and underlying (bottom) beds with a lineal contact. The bottom domain has a weakening circular hole with a multi-layered circular reinforcement which models lining of an underground structure. The formulated problems are solved using the mathematical apparatus including complex-variable functions, Kolosov–Muskhelishvili method, Laurent series and Cauchy-type integrals. The external effects conditioned by overlying rock weight and groundwater pressure are considered as initial stress fields, and the conditions of continuity of displacement vectors and total stresses are set at the boundary of the domains in contact. The obtained solution features a good iterative convergence when at each stage of approximation, a problem on an unsupported circular hole in a full uniform plane is solved at the boundary conditions involving additional functions reflective of the influence of the nonuniformity of the medium and the multi-layered ring, which are adjusted in the course of calculations. The computational process is controlled via testing the accuracy of fulfillment of the boundary conditions, and is terminated when the difference of the calculated stresses and displacements in neighbor iterations is not higher than a preset small. The method is implemented as an original computer program system which allows efficient multivariate calculations for both theoretical and practical purposes. Some case-studies illustrate capabilities of the proposed method and the main results of the stress state analysis of the underground structure and enclosing rock mass under discussion.

1. Bulychev N. S., Fotieva N. N., Streltsov E. V. Permanent Mine Support System Design and Engineering. Moscow : Nedra, 1986. 288 p.
2. Baklashov I. V., Kartoziya B. A. Mechanics of Underground Structures and Designs of Support Systems : Textbook. Moscow : Nedra, 1984. 415 p.
3. Zaslavskiy Yu. Z., Mostkov V. N. Support of Underground Structures. Moscow : Nedra, 1979. 325 p.
4. Pleshko M. S., Abramchuk K. V., Kazintsev I. Yu. Transportation tunnels in the Crimea : The past, the present and the future. Metro i tonneli. 2021. No. 1. pp. 24–28.
5. Zaslavskiy Yu. Z., Lopukhin E. A., Druzhko E. B., Kachan I. V. Injection Reinforcement of Rocks. Moscow : Nedra, 1984. 177 p.
6. Antsiferov S. V., Feklin A. A. Investigation of the effect of reinforcing cementation of rocks on the stress state of parallel tunnel linings. Izvestiya Tulskogo gosudarstvennogo universiteta. Nauki o Zemle. 2023. No. 3. pp. 475–491.
7. Antsiferov S. V., Kudryavtsev M. A. The method of geomechanical justification of stability the soil of slopes accommodating horizontal workings located parallel to the earth surfaces. Gornyi Zhurnal. 2026. No. 3. pp. 26–32.
8. Deev P. V., Tsukanov A. A. Impact of weakened rock layer on displacement of mine opening boundary. Socio-Economic and Environmental Problems of the Mining Industry, Building and Energetics : Proceedings of the 17st International Conference on the Mining Industry, Building and Energetic Problems. Tula : TulGU, 2021. pp. 602–607.
9. Pleshko M. S., Pankratenko A. N., Nasonov A. A., Isaev A. S. Geomechanical monitoring and stress–strain analysis of lining in ultra deep mine shafts. Eurasian Mining. 2023. No. 1. pp. 13–19.
10. Kumar B., Sahoo J. P. Support pressure for circular tunnels in two layered undrained clay. Journal of Rock Mechanics and Geotechnical Engineering. 2020. Vol. 12, Iss. 1. pp. 135–148.
11. Sammal A. S., Starykh M. V. , Portnova A. V. Evaluating the precision of results of parallel tunnel lining calculation by numerical and analytical methods. Izvestiya vuzov. Gornyi zhurnal. 2 025. No. 2. pp. 77–87.
12. Do N.-A., Dias D. Tunnel lining design in multi-layered grounds. Tunnelling and Underground Space Technology. 2018. Vol. 81. pp. 103–111.
13. Zhang Z., Pan Y., Zhang M., Lv X., Jiang K. et al. Complex variable an alytical prediction for ground deformation and lining responses due to shield tunneling considering groundwater level variation in clays. Computers and Geotechnics. 2020. Vol. 120. ID 103443.
14. Muskhelishvili N. I. Some Basic Problems in Mathematical Elasticity : Basic Solutions, Two-Dimensional Elasticity, Torsion and Bending. Moscow : Nauka, 1966. 707 p.