PSI - Issue 32

Mikhail Semin et al. / Procedia Structural Integrity 32 (2021) 180–186 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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assumptions: smallness of the ratio b/a , piecewise linear cohesion function c(r) along the radial coordinate r with a maximum at point ( ) / 2 r b a   , constant angle φ of internal friction. A more accurate calculation of the effect of cohesion distribution non-uniformity in the frozen soil can be done using the integral equation (11). 3. Conclusion The theoretical analysis of the effect of non-uniformity of the frozen soil strength properties on FW thickness was carried out. The condition of the limiting stress state was used to calculate the FW thickness. The main conclusions of the study are presented below:  An integral function was obtained to calculate the FW thickness by strength given the arbitrary radial non uniformity of the cohesion in the frozen soil volume.  An approximate formula is proposed for calculating the FW thickness in the case of a piecewise linear cohesion function of the radial coordinate.  The non-uniformity of the cohesion in the FW volume was shown to have a negative effect and lead to a decrease in the maximum load the FW of the given thickness could withstand. At that, the reduction of the maximum load was proportional to the maximum variation of cohesion in the frozen soil volume.  The solution of the problem is sensitive to the method of setting non-uniformity of the cohesion in the frozen soil volume. Acknowledgements This study was carried out with the financial support of the Russian Science Foundation (project No. 17-11 01204). References Akagawa, S., Nishisato, K., 2019. Tensile strength of frozen soil in the temperature range of the frozen fringe, Cold regions science and technology 57, 13-22. Alzoubi, M.A., Xu, M., Hassani, F.P., Poncet, S., Sasmito,A.P., 2020. Artificial ground freezing: A review of thermal and hydraulic aspects, Tunnelling and Underground Space Technology 104, 103534. Brovka, G.P. Research report. Laboratory geomechanical studies of soil core samples from the Darasinsky mine at various negative temperatures, Minsk, Institute of Nature Management of the National Academy of Sciences of Belarus,Nov. 2020. Jessberger, H. L., 1981. A state-of-the-art report. Ground freezing: Mechanical properties, processes and design. Engineering 29, 5-30. Kostina, A., Zhelnin, M., Plekhov, O., Panteleev, I., Levin, L., 2018. Creep behavior of ice-soil retaining structure during shaft sinking, Procedia Structural Integrity 13, 1273-1278. Kostina, A., Zh elnin, M., Plekhov, O., Panteleev, I., Levin, L., Semin, M., 2020. An Applicability of Vyalov’s equations to ice wall strengt h estimation. Frattura ed IntegritàStru tturale 14(53), 394-405. Levin, L.Y., Semin, M.A., Plekhov, O.A., 2018. Comparative analysis of existing methods for calculating frozen wall thickness for mine shafts under construction, Construction and Geotechnics 9, 93-103. Sanger, F.J., Sayles, F.H., 1979.Thermal and rheological computations for artificially frozen ground construction, Engineering geology 13, 311 337. Semin, M.A., Bogomyagkov, A.V., Levin, L.Y., 2020.Theoretical analysis of frozen wall dynamics during transition to ice holding stage, Journal of Mining Institute 243, 319 – 328. Tsytovich,N.A., 1960.Bases and foundations on frozen soil. National Academy of Sciences, National Research Council, 1960. Vyalov, S.S., 1978.Rheological fundamentals of soil mechanics. Higher. school, Moscow, pp. 148. Xu, X., Wang, Y., Bai, R., Fan, C., Hua, S., 2016. Comparative studies on mechanical behavior of frozen natural saline silty sand and frozen desalted silty sand. Cold Regions Science and Technology 132, 81-88. Yang, W.-H., Du, Z.-B., Yang, Z.-J., Bo, D.-L., 2013.Plastic design theory of frozen soil wall based on interaction between frozen soil wall and surrounding rock, Chinese Journal of Geotechnical Engineering 35, 1857 – 1862. Zhang, B., Yang, W., Wang, B., 2018.Plastic design theory of frozen wall thickness in an ultradeep soil layer considering large deformation characteristics, Mathematical Problems in Engineering 2018, 8513413.