2411-3336 2541-9404 Записки Горного института Journal of Mining Institute Санкт-Петербургский горный университет императрицы Екатерины ΙΙ Empress Catherine II Saint Petersburg Mining University 10.31897/PMI.2022.17 pmi-15661 https://pmi.spmi.ru/pmi/article/view/15661 Геотехнология и инженерная геология Geotechnical Engineering and Engineering Geology Method for predicting the stress state of the lining of underground structures of quasi-rectangular and arched forms Метод прогноза напряженного состояния обделки подземных сооружений квазипрямоугольной и арочной форм Karasev Maksim A. Карасев М. А. Karasev Maksim A. karasevma@gmail.com Санкт-Петербургский горный университет (Россия) Saint Petersburg Mining University (Russia) Nguyen Tien Tai Нгуен Тиен Тай Nguyen Tien Tai taitien12@gmail.com 0000-0002-5246-9252 Санкт-Петербургский горный университет (Вьетнам) Saint Petersburg Mining University (Vietnam) 12 10 2022 2022 257 807 821 17 11 2021 06 04 2022 10 11 2022 © Maksim A. Karasev, Tien Tai Nguyen 2022 М. А. Карасев, Тиен Тай Нгуен Maksim A. Karasev, Tien Tai Nguyen CC BY 4.0 https://pmi.spmi.ru/pmi/article/view/15661

Рассмотрен метод прогноза напряженно-деформированного состояния обделок подземных сооружений, форма поперечного сечения которых отлична от кругового очертания. Основной задачей исследования является разработка методики оценки влияния параметров формы поперечного сечения подземных сооружений на напряженное состояние обделки. Для решения поставленной задачи обоснован и развит метод расчета напряженного состояния обделки для тоннелей арочной с обратным сводом и квазипрямоугольной форм. Выполнена апробация методики, которая показала, что точность прогноза напряженного состояния обделки достаточна для выполнения практических расчетов. Предложен алгоритм проведения многовариантного анализа влияния формы поперечного сечения подземных сооружений арочной и квазипрямоугольной форм на напряженное состояние обделки. С использованием разработанного алгоритма выполнены параметрические расчеты и получены закономерности формирования напряженного состояния обделок подземных сооружений для различных инженерно-геологических условий, а также начального поля напряженного состояния. Выполнена количественная оценка влияния геометрических параметров тоннелей на их напряженно-деформированное состояние.

A method for predicting the stress-strain state of the lining of underground structures, the shape of the cross-section of which is different from the circular outline, is considered. The main task of the study is to develop a methodology for assessing the influence of the parameters of the cross-section shape of underground structures on the stress state of the lining. To solve this problem, a method for calculating the stress state of the lining for arched tunnels with a reverse arch and quasi-rectangular forms is substantiated and developed. The methodology was tested, which showed that the accuracy of the prediction of the stress state of the lining is sufficient to perform practical calculations. An algorithm for multivariate analysis of the influence of the cross-sectional shape of underground structures of arched and quasi-rectangular shapes on the stress state of the lining is proposed. Parametric calculations were performed using the developed algorithm and regularities of the formation of the stress state of the lining of underground structures for various engineering and geological conditions, as well as the initial stress state field, were obtained. A quantitative assessment of the influence of geometric parameters of tunnels on their stress-strain state was performed.

 Ключевые слова тоннель обделка напряженное состояние взаимодействие нагрузка метод оптимизации формы поперечное сечение грунтовый массив Keywords tunnel lining stress state interaction load shape optimization method cross-section soil mass Tatiya R. Civil excavations and tunnelling: a practical guide. London: Thomas Telford, 2005. 322 p. Tatiya R. Civil excavations and tunnelling: a practical guide. London: Thomas Telford, 2005, p. 322. Yingyongrattanakul N., Adachi T., Tateyama K., Kurahashi M. Optimal shape of underground structure // Modern Tunneling Science and Technology. London: Taylor & Francis, 2001. 628 p. Yingyongrattanakul N., Adachi T., Tateyama K., Kurahashi M. Optimal shape of underground structure. Modern Tunneling Science and Technology. London: Taylor & Francis, 2001, p. 628. Господариков А.П., Выходцев Я.Н., Зацепин М.А. Математическое моделирование воздействия сейсмовзрывных волн на горный массив, включающий выработку // Записки Горного института. 2017. Т. 226. С. 405-411. DOI: 10.25515/PMI.2017.4.405 Gospodarikov A.P., Vykhodtsev Y.N., Zatsepin M.A. Mathematical modeling of seismic explosion waves impact on rock mass with a working. Journal of Mining Institute. 2017. Vol. 226, p. 405-411. DOI: 10.25515/PMI.2017 Саммаль А.С., Фотиева Н.Н., Булычев Н.С., Хренов С.И. Расчет тоннельных обделок переменной толщины с учетом влияния земной поверхности // Записки Горного института. 2004. Т. 156. С. 24-26. Sammal A.S., Fotieva N.N., Bulychev N.S., Khrenov S.I. Calculation of tunnel linings of variable thickness taking into account the influence of the Earth's surface. Journal of Mining Institute. 2004. Vol. 156, p. 24-26 (in Russian). Protosenya A.G., Lebedev M.O. Calculation of the Loads on Linings of Subway Tunnels Constructed in Physically Nonlinear Soil Masses // Journal of Mining Science. 2002. Vol. 38. Iss. 5. P. 418-424. DOI: 10.1023/A:1023975313128 Protosenya A.G., Lebedev M.O. Calculation of the Loads on Linings of Subway Tunnels Constructed in Physically Nonlinear Soil Masses. Journal of Mining Science. 2002. Vol. 38. Iss. 5, p. 418-424. DOI: 10.1023/A:1023975313128 Protosenya A.G., Karasev M.A., Belyakov N.A. Elastoplastic problem for noncircular openings under Coulomb’s criterion // Journal of Mining Science. 2016. Vol. 1. P. 53-61. DOI: 10.1134/S1062739116010125 Protosenya A.G., Karasev M.A., Belyakov N.A. Elastoplastic problem for noncircular openings under Coulomb’s criterion. Journal of Mining Science. 2016. Vol. 1, p. 53-61. DOI: 10.1134/S1062739116010125 Belyakov N.A., Smirnova O.M., Alekseev A.V., Tan H. Numerical Simulation of the Mechanical Behavior of Fiber-Reinforced Cement Composites Subjected Dynamic Loading // Applied Sciences. 2021. Vol. 11. Iss. 3. № 1112. DOI: 10.3390/app11031112 Belyakov N.A., Smirnova O.M., Alekseev A.V., Tan H. Numerical Simulation of the Mechanical Behavior of Fiber-Reinforced Cement Composites Subjected Dynamic Loading. Applied Sciences. 2021. Vol. 11. Iss. 3. N 1112. DOI: 10.3390/app11031112 Nguyen C.T., Gospodarikov A.P. Hyperstatic reaction method for calculations of tunnels with horseshoe-shaped cross-section under the impact of earthquakes // Earthquake Engineering and Engineering Vibration. 2020. Vol. 19. P. 179-188. Nguyen C.T., Gospodarikov A.P. Hyperstatic reaction method for calculations of tunnels with horseshoe-shaped cross-section under the impact of earthquakes. Earthquake Engineering and Engineering Vibration. 2020. Vol. 19, p. 179-188. DOI: 10.1007/s11803-020-0555-0 DOI: 10.1007/s11803-020-0555-0 Fan Wang, Biancai Gou, Yawei Qin et al. Modeling tunneling-induced ground surface settlement development using a wavelet smooth relevance vector machine. Computers and Geotechnics. 2013. Vol. 54, p. 125-132. DOI: 10.1016/j.compgeo.2013.07.004 Fan Wang, Biancai Gou, Yawei Qin et al. Modeling tunneling-induced ground surface settlement development using a wavelet smooth relevance vector machine // Computers and Geotechnics. 2013. Vol. 54. P. 125-132. DOI: 10.1016/j.compgeo.2013.07.004 Bezrodnyi K.P., Lebedev M.O. About rock pressure loads on tunnel linings constructed using trenchless method. Journal of Mining Institute. 2017. Vol. 228, p. 649-653. DOI: 10.25515/PMI.2017.6.649 Безродный К.П., Лебедев М.О. О нагрузках от горного давления на обделки тоннелей закрытого способа работ // Записки Горного института. 2017. Т. 228. С. 649-653. DOI: 10.25515/PMI.2017.6.649 Arnau O., Molins C. Experimental and analytical study of the structural response of segmental tunnel linings based on an in-situ loading test. Part 1: Test configuration and execution. Tunnelling and Underground Space Technology. 2011. Vol. 26. Iss. 6, p. 764-777. DOI: 10.1016/j.tust.2011.05.002 Arnau O., Molins C. Experimental and analytical study of the structural response of segmental tunnel linings based on an in-situ loading test. Part 1: Test configuration and execution// Tunnelling and Underground Space Technology. 2011. Vol. 26. Iss. 6. P. 764-777. DOI: 10.1016/j.tust.2011.05.002 Petrakov D.G., Penkov G.M., Zolotukhin A.B. Experimental study of the effect of rock pressure on sandstone, permeability. Journal of Mining Institute. 2022. Vol. 254, p. 244-251. DOI: 10.31897/PMI.2022.24 Петраков Д.Г., Пеньков Г.М., Золотухин А.Б. Экспериментальное исследование влияния горного давления на проницаемость песчаника // Записки Горного института. 2022. Т. 254. С. 244-251. DOI: 10.31897/PMI.2022.24 Do N.A., Dias D., Oreste P., Maigre I.D. The behaviour of the segmental tunnel lining studied by the hyperstatic reaction method. European Journal of Environmental and Civil Engineering. 2014. Vol. 18. Iss. 4, p. 489-510. DOI: 10.1080/19648189.2013.872583 Do N.A., Dias D., Oreste P., Maigre I.D. The behaviour of the segmental tunnel lining studied by the hyperstatic reaction method // European Journal of Environmental and Civil Engineering. 2014. Vol. 18. Iss. 4. P. 489-510. DOI: 10.1080/19648189.2013.872583 Blom C.B. Design philosophy of concrete linings for tunnel in soft soils. Delft, Netherlands: Delft University, 2002. Blom C.B. Design philosophy of concrete linings for tunnel in soft soils. Delft, Netherlands: Delft University, 2002. Xiaojun Li, Zhiguo Yan, Zhen Wang et al. Experimental and analytical study on longitudinal joint opening of concrete segmental lining. Tunnelling and Underground Space Technology. 2015. Vol. 46, p. 52-63. DOI: 10. 1016/j.tust.2014.11.002 Xiaojun Li, Zhiguo Yan, Zhen Wang et al. Experimental and analytical study on longitudinal joint opening of concrete segmental lining // Tunnelling and Underground Space Technology. 2015. Vol. 46. P. 52-63. DOI: 10.1016/j.tust.2014.11.002 Liang Lu, Xilin Lu, Peifang Fan. Full-Ring Experimental Study of the Lining Structure of Shanghai Changjiang Tunnel. Journal of Civil Engineering and Architecture. 2011. Vol. 5. Iss. 8, p. 732-739. DOI: 10.17265/1934-7359/2011.08.007 Liang Lu, Xilin Lu, Peifang Fan. Full-Ring Experimental Study of the Lining Structure of Shanghai Changjiang Tunnel // Journal of Civil Engineering and Architecture. 2011. Vol. 5. Iss. 8. P. 732-739. DOI: 10.17265/1934-7359/2011.08.007 Nakamura H., Kubota T., Furukawa M., Nakao T. Unified construction of running track tunnel and crossover tunnel for Unified construction of running track tunnel and crossover tunnel for. Tunnelling and Underground Space Technology. 2003. Vol. 18, p. 253-262. DOI: 10.1016/S0886-7798(03)00034-8 Nakamura H., Kubota T., Furukawa M., Nakao T. Unified construction of running track tunnel and crossover tunnel for Unified construction of running track tunnel and crossover tunnel for // Tunnelling and Underground Space Technology. 2003. Vol. 18. P. 253-262. DOI: 10.1016/S0886-7798(03)00034-8 Xin Huang, Yeting Zhu, Zixin Zhang et al. Mechanical behaviour of segmental lining of a sub-rectangular shield tunnel under self-weight. Tunnelling and Underground Space Technology. 2018. Vol. 74, p. 131-144. DOI: 10.1016/j.tust.2018.01.016 XinHuang, YetingZhu, ZixinZhang et al. Mechanical behaviour of segmental lining of a sub-rectangular shield tunnel under self-weight // Tunnelling and Underground Space Technology. 2018. Vol. 74. P. 131-144. DOI: 10.1016/j.tust.2018.01.016 Xian Liu, Zhen Liu, Yuhang Ye et al. Mechanical behavior of quasi-rectangular segmental tunnel linings: Further insights from full-scale ring tests. Tunnelling and Underground Space Technology. 2018. Vol. 79, p. 304-318. DOI: 10.1016/j.tust.2018.05.016 Xian Liu, Zhen Liu, Yuhang Ye et al.Mechanical behavior of quasi-rectangular segmental tunnel linings: Further insights from full-scale ring tests // Tunnelling and Underground Space Technology. 2018. Vol. 79. P. 304-318. DOI: 10.1016/j.tust.2018.05.016 Xian Liu, Yuhang Ye, Zhen Liu, Dezhong Huang. Mechanical behavior of Quasi-rectangular segmental tunnel linings: First results from full-scale ring tests. Tunnelling and Underground Space Technology. 2018. Vol. 71, p. 440-453. DOI: 10.1016/j.tust.2017.09.019 Xian Liu, Yuhang Ye, Zhen Liu, Dezhong Huang. Mechanical behavior of Quasi-rectangular segmental tunnel linings: First results from full-scale ring tests // Tunnelling and Underground Space Technology. 2018. Vol. 71. P. 440-453. DOI: 1016/j.tust.2017.09.019 Trushko V.L., Protosenya A.G., Trushko O.V. Stress-strain behavior of the workings during the rich iron ores development under the confined aquifers. International Journal of Applied Engineering Research. 2016. Vol. 11. Iss. 23, p. 11153-11164. Trushko V.L., Protosenya A.G., Trushko O.V. Stress-strain behavior of the workings during the rich iron ores development under the confined aquifers // International Journal of Applied Engineering Research. 2016. Vol. 11. Iss. 23. P. 11153-11164. Feng Yang, Xinlei Sun, Jiahong Zou, Xiangcou Zheng. Analysis of an elliptical tunnel affected by surcharge loading. Proceedings of the Institution of Civil Engineers – Geotechnical Engineering. 2019. Vol. 172. Iss. 4, p. 312-319. DOI: 10.1680/jgeen.16.00122 Feng Yang, Xinlei Sun, Jiahong Zou, Xiangcou Zheng. Analysis of an elliptical tunnel affected by surcharge loading // Proceedings of the Institution of Civil Engineers – Geotechnical Engineering. 2019. Vol. 172. Iss. 4. P. 312-319. DOI: 1680/jgeen.16.00122 Palassi M., Mohebbi M. Design of Lining of Tunnels Excavated in Soil and Soft Rock. The Electronic Journal of Geotechnical Engineering. 2008. Vol. 3, p. 1-15. Palassi M., Mohebbi M. Design of Lining of Tunnels Excavated in Soil and Soft Rock // The Electronic Journal of Geotechnical Engineering. 2008. Vol. 3. P. 1-15. Protosenya A., Vilner M. Assessment of excavation intersections’ stability in jointed rock masses using the discontinuum approach. Rudarsko-geološko-naftni zbornik. 2022. Vol. 38 (2), p. 137-147. DOI: 10.17794/rgn.2022.2.12 Protosenya A., Vilner M. Assessment of excavation intersections’ stability in jointed rock masses using the discontinuum approach // Rudarsko-geološko-naftni zbornik. 2022. Vol. 38 (2). P. 137-147. DOI: 10.17794/rgn.2022.2.12 Wang H., Zeng G., Jiang M. Analytical stress and displacement around non-circular tunnels in semi-infinite ground. Applied Mathematical Modelling. 2018. Vol. 63, p. 303-328. DOI: 10.1016/j.apm.2018.06.043 Wang H., Zeng G., JiangM. Analytical stress and displacement around non-circular tunnels in semi-infinite ground // Applied Mathematical Modelling. 2018. Vol. 63. P. 303-328. DOI: 10.1016/j.apm.2018.06.043 Abdellah W.R., Ali M.A., Yang H.S. Studying the effect of some parameters on the stability of shallow tunnels. Journal of Sustainable Mining. 2018. Vol. 17. Iss. 1. P. 20-33. DOI: 10.1016/j.jsm.2018.02.001 Abdellah W.R., Ali M.A., Yang H.S. Studying the effect of some parameters on the stability of shallow tunnels // Journal of Sustainable Mining. 2018. Vol. 17. Iss. 1. P. 20-33. DOI: 10.1016/j.jsm.2018.02.001 Rostami A., Asghari N., Ziarati M.A. et al. Investigating Effect of Tunnel Gate Investigating Effect of Tunnel Gate Inserted Forces on Its Coverage and Soil Surface Settlement. Journal of Civil Engineering. 2016. Vol. 6. Iss. 3. p. 358-369. DOI: 10.4236/ojce.2016.63030 Rostami A., Asghari N., Ziarati M.A. et al. Investigating Effect of Tunnel Gate Investigating Effect of Tunnel Gate Inserted Forces on Its Coverage and Soil Surface Settlement // Journal of Civil Engineering. 2016. Vol. 6. Iss. 3. P. 358-369. DOI: 10.4236/ojce.2016.63030 Vinod M., Khabbaz H. Comparison of rectangular and circular bored twin tunnels in weak ground. Underground Space. 2019. Vol. 4. Iss. 4, p. 328-339. DOI: 10.1016/j.undsp.2019.03.004 Vinod M., KhabbazH. Comparison of rectangular and circular bored twin tunnels in weak ground // Underground Space. 2019. Vol. 4. Iss. 4. P. 328-339. DOI: 10.1016/j.undsp.2019.03.004 Do N.A., Dias D., Zhang Z. et al. Study on the behavior of squared and sub-rectangular tunnels using the Hyperstatic Reaction Method. Transportation Geotechnics. 2020. Vol. 22. N 100321. DOI: 10.1016/j.trgeo.2020.100321 Do N.A., Dias D., Zhang Z. et al. Study on the behavior of squared and sub-rectangular tunnels using the Hyperstatic Reaction Method // Transportation Geotechnics. 2020. Vol. 22. № 100321. DOI: 10.1016/j.trgeo.2020.100321 Oreste P. A numerical approach to the hyperstatic reaction method for the dimensioning of tunnel supports. Tunnelling and Underground Space Technology. 2007. Vol. 22. Iss. 2, p. 185-205. DOI: 10.1016/j.tust.2006.05.002 Oreste P. A numerical approach to the hyperstatic reaction method for the dimensioning of tunnel supports // Tunnelling and Underground Space Technology. 2007. Vol. 22. Iss. 2. P. 185-205. DOI: 10.1016/j.tust.2006.05.002 Huebner K.H., Dewhirst D.L., Smith D.E., Byrom T.G. The finite element method for engineers. New York: John Wiley and Sons, 2001, p. 744. Huebner K.H., Dewhirst D.L., Smith D.E., Byrom T.G. The finite element method for engineers. New York: John Wiley and Sons, 2001. 744 p. Baklashov I.V., Kartoziya B.A. Mechanics of underground structures and the construction of supports. Moscow: Student, 2012, p. 543 (in Russian). Баклашов И.В., Картозия Б.А. Механика подземных сооружений и конструкции крепей. М.: Студент, 2012. 543 c. Bulychev N.S. Mechanics of underground structures. Moscow: Nedra, 1994, p. 382 (in Russian). Булычев Н.С. Механика подземных сооружений. М.: Недра, 1994. 382 c. Kolymbas D. Tunnelling and Tunnel Mechanics. A rational Approach to Tunneling. Berlin: Springer, 2005, p. 439. Kolymbas D. Tunnelling and Tunnel Mechanics. A rational Approach to Tunneling. Berlin: Springer, 2005. 439 p. Széchy K. The Art of Tunnelling. Budapest: Akadémiai Kiadó, 1973, p. 1097. Széchy K. The Art of Tunnelling. Budapest: Akadémiai Kiadó, 1973. 1097 p. Takano Y.H. Guidelines for the design of shield tunnel lining. Tunneling and Underground Space Technology. 2000. Vol. 15. Iss. 3, p. 303-331. DOI: 10.1016/S0886-7798(00)00058-4 Takano Y.H. Guidelines for the design of shield tunnel lining // Tunneling and Underground Space Technology. 2000. Vol. 15. Iss. 3. P. 303-331. DOI: 10.1016/S0886-7798(00)00058-4 Do N.A., Dias D. Tunnel lining design in multi-layered grounds. Tunnelling and Underground Space Technology. 2018. Vol. 81, p. 103-111. DOI: 10.1016/j.tust.2018.07.005 Do N.A., Dias D. Tunnel lining design in multi-layered grounds // Tunnelling and Underground Space Technology. 2018. Vol. 81. P. 103-111. DOI: 10.1016/j.tust.2018.07.005 Nguyen T.T., Do N.A., Karasev M.A. et al. Influence of tunnel shape on tunnel lining behavior. Proceedings of the Institution of Civil Engineers – Geotechnical Engineering. 2021. Vol. 174. Iss. 4, p. 355-371. DOI: 10.1680/jgeen.20.00057 Nguyen T.T., Do N.A., Karasev M.A. et al. Influence of tunnel shape on tunnel lining behaviour // Proceedings of the Institution of Civil Engineers – Geotechnical Engineering. 2021. Vol. 174. Iss. 4. P. 355-371. DOI: 10.1680/jgeen.20.00057 Nguyen Tai Tien, Karasev M.A. Optimization of Geometry Design of Quasi-Rectangular Section Tunnel by the Force Criterion. Mining Informational and Analytical Bulletin. 2021. Vol. 6, p. 59-71 (in Russian). DOI: 10.25018/0236_1493_2021_6_0_59 Нгуен Т.Т., Карасев М.А. Расчет оптимальных геометрических параметров тоннеля квазипрямоугольного поперечного очертания по силовому фактору // Горный информационно-аналитический бюллетень. 2021. Т. 6. С. 59-71. DOI: 10.25018/0236_1493_2021_6_0_59 Du D., Dias D., Do N. Lining performance optimization of sub-rectangular tunnels using the Hyperstatic Reaction Method. Computers and Geotechnics. 2020. Vol. 117. N 103279. DOI: 10.1016/j.compgeo.2019.103279 Du D., Dias D., Do N. Lining performance optimization of sub-rectangular tunnels using the Hyperstatic Reaction Method // Computers and Geotechnics. 2020. Vol. 117. № 103279. DOI: 10.1016/j.compgeo.2019.103279 Gospodarikov P., Zatsepin M. Mathematical modeling of boundary problems in geomechanics. Gornyi zhurnal. 2019. Vol. 12, p. 16-20 (in Russian). DOI: 10.17580/gzh.2019.12.03 Господариков А.П., Зацепин М.А. Математическое моделирование нелинейных краевых задач геомеханики // Горный журнал. 2019. № 12. С. 16-20. DOI: 10.17580/gzh.2019.12.03