Analytical determination of the stress-strain state of soil mass during tunnelling

Introduction. One of the effective approaches to assessing the impact of tunnel construction works involves a comprehensive approach to problem-solving, including determination of the face-support pressure to ensure the stability of the tunnel face and assessment of additional surface movements that occur during tunnel construction. This approach is justified by the fact that actual displacements can be close to predicted ones when the optimal face-support pressure is selected and there is no face loss of soil, which could lead to unforeseen deformations. However, it should be noted that the method for calculating pressure presented in the current standard is a preliminary forecast and requires constant adjustment of the pressure during tunnel construction works.

Materials and methods. In this work, the authors adapted Melan’s problem formulation with a horizontal load parallel to the surface to assess the change in the stress-strain state of the soil mass before tunnel face excavation due to the application of the face-support pressure. The problem formulation corresponds to the stage of work preparation before excavation of the soil for the installation of a precast concrete lining ring into its design position.

Results. Based on the analytical equations formulated in the MathCAD software environment, isopoles of vertical and horizontal stresses, and vertical deformations were created. The obtained isopoles were compared with isopoles generated in the Plaxis 2D software using similar parameters to validate the results. Additionally, isopoles of the soil mass under the influence of the face-support pressure, considering self-weight stresses, were obtained to establish a more realistic stress-strain state of the mass in which a tunnel is being constructed.

Conclusions. The analysis of the research results has shown that the isopoles are quantitatively and qualitatively similar to each other. The method proposed by the authors can be adapted with appropriate modifications to adjust the face-support pressure during construction, which is necessary both to ensure the stability of the tunnel face during construction and to minimize the impact of the face-support pressure on the ground surface.

1. Mazein S.V., Voznesenskiy A.S. Experience of shield tunneling with hydro face-support pressure. Metro and Tunnels. 2019; 1:14-17. EDN PPYGWR. (rus.).

2. Protosenya A.G., Belyakov N.A., Tkhai D.N. Development of a method for forecasting face-support pressure and ground settlement during tunnel construction with mechanized tunneling complexes. Journal of Mining Institute. 2015; 211:53-63. EDN TQMGPV. (rus.).

3. Protod’yakonov M.M. Pressure of rock formations on mine supports. Mining Journal. 1907. (rus.).

4. Ter-Martirosyan A.Z., Cherkesov R.H., Isaev I.O., Shishkina V.V. Surface settlement during tunneling: field observation analysis. Applied Sciences. 2022; 12(19):9963. DOI: 10.3390/app12199963

5. Ter-Martirosyan A.Z., Cherkesov R.H., Isaev I.O., Rud V.V. The actual volume loss of soil coefficient for tunnels in cohesive and rock soils. Housing Construction. 2023; 9:61-73. DOI: 10.31659/0044-4472-2023-9-61-73. EDN UBBWQA. (rus.).

6. Horn N. Horizontal earth pressure on perpendicular tunnel face. Proceedings of the Hungarian National Conference of the Foundation Engineer Industry. 1961.

7. Janssen H.A. Experiments on grain pressure in silo cells. Journal of the Association of German Engineers. 1895; 35:1045-1049.

8. Frid M. Results of experiments on the pressure of grain on the bottom and walls of deep vessels. Flour and Food Industry. 1890; 921-933. (rus.).

9. Anagnostou G., Kovari K. Face stability conditions with earth-pressure-balanced shields. Tunnelling and Underground Space Technology. 1996; 11(2):165-173. DOI: 10.1016/0886-7798(96)00017-x

10. Anagnostou G. The contribution of horizontal arching to tunnel face stability. Geotechnik. 2012; 35(1):34-44. DOI: 10.1002/gete.201100024

11. Leca E., Dormieux L. Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material. Géotechnique. 1990; 40(4):581-606. DOI: 10.1680/geot.1990.40.4.581

12. Yuan S., Feng D., Zhang S., Xing Y., Ke Z. Stability analysis of shield tunnel face considering spatial variability of hydraulic parameters. Rock and Soil Mechanics. 2022; 43(11):3153-3162. DOI: 10.16285/j.rsm.2021.2200

13. Chang Y., Cao P., Zhang J., Fan Z., Xie W., Liu Z. et al. Face stability of tunnel in multi-stratum: limit analysis and numerical simulation. Geotechnical and Geological Engineering. 2023; 41(5):3203-3215. DOI: 10.1007/s10706-023-02453-1

14. Wang W., Liu H., Deng R., Wang Y. Active stability analysis of 3D tunnel face in nonhomogeneous and anisotropic soils. Geotechnical and Geological Engineering. 2023; 41(5):3013-3033. DOI: 10.1007/s10706-023-02442-4

15. Melan E. Der Spannungszustand der durch eine Einzelkraft im Innern beanspruchten Halbscheibe. ZAMM — Journal of Applied Mathematics and Mechanics. Zeitschrift für Angewandte Mathematik und Mechanik. 1932; 12(6):343-346. DOI: 10.1002/zamm.19320120603

16. Airy G.B. On the strains in the interior of beams. Proceedings of the Royal Society of London. 1863; 12:304-306. DOI: 10.1098/rspl.1862.0068

17. Hanna A.M., Hadid W.H. New models for shallow foundations. Mathematical Modelling. 1987; 9(11):799-811. DOI: 10.1016/0270-0255(87)90500-8

18. Ter-Martirosian A.Z., Ter-Martirosian Z.G., Luzin I.N. Stress-strain condition of base of deep foundations. Bulletin of Perm State Technical University. Construction and Architecture. 2017; 8(2):96-103. DOI: 10.15593/2224-9826/2017.2.09. EDN YYZKHJ. (rus.).

19. Ter-Martirosyan Z.G., Vanina Y.V. Impact of a deep foundation on enclosing wall structure of excavation. Journal of Physics: Conference Series. 2021; 1928(1):012004. DOI: 10.1088/1742-6596/1928/1/012004

20. Hu Q. Retaining structure force-deformation analysis model for an ultradeep foundation pit. Mathe-matical Problems in Engineering. 2013; 2013:1-18. DOI: 10.1155/2013/549491

21. Zertsalov M.G., Kazachenko S.A. Numerical-analytical method of engineering assessment of the impact of the development of the pit on the movement of the adjacent soil mass, taking into account the rigidity of the fencing of the pit. Mechanics of Composite Materials and Structures. 2021; 27(3):396-409. DOI: 10.33113/mkmk.ras.2021.27.03.396_409.07. EDN FPQJTC. (rus.).