Tula State University (Tula, Russia)

P. V. Deev, Professor of Department, Doctor of Engineering Sciences, dodysya@yandex.ru
K. S. Kaplunov, Associate Professor
D. S. Serebrennikov, Associate Professor

Strong earthquakes may cause collapse of mine workings and damage to support structures, thus the design of such objects placed in seismically active regions must take into account the possibility of seismic waves’ action. Currently, the most advanced method for evaluation of the stress state of rock mass and underground structures is numerical modeling, which allows using various mechanical models and a wide range of dynamic impact parameters. But using numerical technique in multivariate calculations, for example, in order to find out the most unfavorable seismic impact, takes too much time to be suitable for practical use. In such cases analytical methods combined with the pseudostatic approach are preferable. The pseudostatic analysis needs values of seismic stresses applied to the design scheme as the input data, and so a suitable technique for stress determination is required. Finding the stresses appearing in layered or fractured rock mass during seismic wave propagation is a special problem, because deformation properties of such rocks strongly depend on the direction, and the formulas for stress calculation are more complex than in the case of isotropic media. The study examines the propagation of plane harmonic waves in a transversely isotropic elastic medium modeling a fractured or layered rock mass. The formulas obtained allow determining the maximum normal and shear stresses appearing in the plane perpendicular to the isotropy plane during the propagation of quasi-longitudinal and quasi-shear waves caused by an earthquake of a certain intensity. The dependences of the stress values on the angle between the wave direction and the isotropy plane are studied; the comparison of seismic stresses arising in transversely isotropic and isotropic rock masses is performed. The values of seismic stresses in an anisotropic rock mass obtained by existing and proposed methods have been evaluated as well.

1. Owen G. N., Scholl R. E. Earthquake engineering of large underground structures : Final Report No. FHWA/RD-80/195. Federal Highway Administration and National Science Foundation, 1981. 287 p.
2. Hashash Y. M. A., Hook J. J., Schmidt B., Yao John I-Chiang Yao. Seismic design and analysis of underground structures. Tunnelling and Underground Space Technology. 2001. Vol. 16. pp. 247–293.
3. Guidelines for the Analysis and Design of Transport Tunnels in High-Seismicity Regions : Guidance manual. Moscow, 2018. 165 p.
4. Basirat R. Analysis of tunnel lining internal forces under the influence of S and P-waves: An analytical solution and quasi-static numerical method. Rock Mechanics Bulletin. 2025. Vol. 4, Iss. 1. ID 100168.
5. Napetvaridze Sh. G. Seismic resistance of hydraulic structures. Moscow : Gosstroyizdat, 1959. 216 p.
6. Landau L. D., Lifshits E. M. Theoretical physics : Tutorial. 5th ed. Moscow : URSS, 2026. Vol. 7. 264 p.
7. Dorman I. Ya. Seismic resistance of transport tunnels. 2nd enlarged and revised edition. Moscow : TIMR, 2000. 307 p.
8. Fotieva N. N., Bulychev N. S., Deev P. V. Design of linings of parallel shallow tunnels subjected to seismic action of earthquakes. Izvestiya Tulskogo gosudarstvennogo universiteta. Nauki o Zemle. 2015. No. 3. pp. 118–125.
9. Maji V. B. Rock Tunnel Behaviour Under Seismic Loading. Indian Geotechnical Journal. 2024. Vol. 54, Iss. 5. pp. 1873–1883.
10. Zhang X., Jiang Y., Chen L., Wang X., Golsanami N. et al. Anti-plane seismic performance of a shallow-buried tunnel with imperfect interface in anisotropic half-space. Tunnelling and Underground Space Technology. 2021. Vol. 112. ID 103906.
11. Shu X., Zhu Z., Qu S., He L., Zeng H. et al. Anisotropic characteristics and deformation behaviors of layered rocks surrounding tunnel: A review. Journal of Rock Mechanics and Geotechnical Engineering. 2025. Vol. 17, Iss. 12. pp. 8198–8223.
12. Erzhanov Zh. S., Aytaliev Sh. M., Masanov Zh. K. Seismic stress state of underground structures in anisotropic layered rock mass. Alma-Ata : Nauka, 1980. 211 p.
13. Carcione J. M. Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media : Handbook of Geophysical Exploration. 2nd ed., revised and extended. Amsterdam : Elsevier, 2007. 534 p.
14. SP 14.13330.2018. Con struction in seismic areas (SNiP II-7-81). Moscow : Stroyinform, 2018. 122 p.