PSI - Issue 32

M. Zhelnin et al. / Procedia Structural Integrity 32 (2021) 71–78 M. Zhelnin/ Structural Integrity Procedia 00 (2021) 000–000

78 8

3. Conclusions In this study numerical simulation of mechanical behavior in the shaft lining during thawing of the frozen wall has been carried out. To perform the simulation a thermo-mechanical model is proposed taking into account latent heat of the phase transition and creep strain of the concrete shell. Moreover, to describe stress-strain state of the concrete shell and the cement grouted soil after elimination of the frozen wall the mechanical part of the model was extended by plastic deformation. Results of the numerical simulation have shown that during thawing of the frozen wall creep strain is evolved in the concrete shell under the lateral pressure. However, the equivalent total strain can change non-monotonically due to the redistribution of the loading throughout the layer of the thawed soil between the external side of the concrete shell and the inner side of the frozen wall. Computation of the stress-strain state in the concrete shell and cement grouted soil under the lateral pressure allows one to conclude that plastic deformation can occur in the shell and grouted soil after elimination of the frozen wall. Maximum equivalent and volumetric plastic strains are reached at the interface between the shell and grouted soil. To prevent plastic deformation of the concrete shell its stiffness has to be reduced or its thickness has to be increased. In the case of stiffness reduction, the limit stress state of the concrete shell can be avoided. However, the plastic deformation of the grouted sand near the outer side of the shell can occur. In case of the increase in thickness up to reasonable values, small plastic strain occurs at the interface between the cast iron tubbing and concrete shell, but the mechanical response of the grouted soil is fully elastic. The stress-strain state of the concrete shell is more sensitive to the stiffness compared with the thickness. Increase in the thickness of the grouted sand layer has small influence on the plastic deformation of the concrete shell. Acknowledgements This research was supported by Russian Science Foundation (Grant No. 17-11-01204). References [1] Jia, Y. D., Stace, R., Williams, A., 2013. Numerical modelling of shaft lining stability at deep mine. Mining Technology 122, 8-19. https://doi.org/10.1179/1743286312Y.0000000022. [2] Fabich, S., Bauer, J., Rajczakowska, M., Świtoń, S., 2015. Design of the shaft lining and shaft stations for deep polymetallic ore deposits: Victoria Mine case study. Mining Science 22, 127-146. https://doi.org/10.5277/msc152213. [3] Walton, G., Kim, E., Sinha, S., Sturgis, G., Berberick, D., 2018. Investigation of shaft stability and anisotropic deformation in a deep shaft in Idaho, United States. International Journal of Rock Mechanics and Mining Sciences 105, 160-171. https://doi.org/10.1016/j.ijrmms.2018.03.017. [4] Wu, Y., Zhu, S. Y., Li, X. Z., Zhang, H., Huang, Z., 2019. Distribution characteristics of the additional vertical stress on a shaft wall in thick and deep alluvium: a simulation analysis. Natural Hazards 96, 353-368. https://doi.org/10.1007/s11069-018-3545-z [5] Oreste, P., Spagnoli, G., Bianco, L.L., 2016. A combined analytical and numerical approach for the evaluation of radial loads on the lining of vertical shafts. Geotechnical and Geological Engineering 34, 1057-1065. https://0.1007/s10706-016-0026-6 [6] Spagnoli, G., Oreste, P., Bianco, L.L., 2017. Estimation of shaft radial displacement beyond the excavation bottom before installation of permanent lining in nondilatant weak rocks with a novel formulation. International Journal of Geomechanics 17, 04017051. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000949 [7] Oreste, P., Spagnoli, G., Ceravolo, L. A., 2019. A numerical model to assess the creep of shotcrete linings. Proceedings of the Institution of Civil Engineers-Geotechnical Engineering 172, 344-354. https://doi.org/10.1680/jgeen.18.00089 [8] Zhang, J. L., Schlappal, T., Yuan, Y., Mang, H. A., Pichler, B., 2019. The influence of interfacial joints on the structural behavior of segmental tunnel rings subjected to ground pressure. Tunnelling and Underground Space Technology 84, 538-556. https://doi.org/10.1016/j.tust.2018.08.025 [9] Liu, W., Zhang, S., Sun, B., Chen, L., 2020. Creep characteristics and time-dependent creep model of tunnel lining structure concrete. Mechanics of Time-Dependent Materials, 1-18. https://doi.org/10.1007/s11043-020-09449-x [10] Li, D., Liu, X., Liu, X., 2015. Experimental study on artificial cemented sand prepared with ordinary Portland cement with different contents. Materials 8, 3960-3974. https://doi.org/10.3390/ma8073960 [11] Sharafi, H., Shekarbeigi, M., 2019. Experimental evaluation of the behavior of Sandy Soil–Cement Mixture. Revista Ingeniería UC 26 258 272. [12] Maghous, S., Consoli, N. C., Fonini, A., Dutra, V. P., 2014. A theoretical–experimental approach to elastic and strength properties of artificially cemented sand. Computers and Geotechnics 62, 40-50. https://doi.org/10.1016/j.compgeo.2014.06.011 [13] Zhou, J., Li, D., 2012. Numerical analysis of coupled water, heat and stress in saturated freezing soil. Cold Regions Science and Technology 72, 43-49. https://doi.org/10.1016/j.coldregions.2011.11.006