Analytical Solution for Radial Displacement–Dependent Earth Pressure Acting on Underwater Rock-Socketed Circular Diaphragm Walls
Publication: International Journal of Geomechanics
Volume 24, Issue 5
Abstract
The distribution of lateral earth pressure acting on underwater rock-socketed circular diaphragm walls was investigated using theoretical analyses. Emphasis was placed on the relationship between the motion modes associated with the magnitude of the radial deflection of the wall and the lateral earth pressure. A framework for determining the distribution of radial displacement–dependent earth pressure based on the horizontal differential element method was introduced. The applicability of the proposed theoretical method was then verified by comparison with results that considered earth pressure in limit state, and radial deflection of the wall and water level. The predicted earth pressure and its distribution were found to be in good agreement with the analytical solutions and observed data. Detailed parametric analyses were further performed to study the impact of soil properties, excavation radius, and water level on the distribution of radial displacement–dependent earth pressure under different radial wall movement modes of a circular retaining structure.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
This research was supported by the National Natural Science Foundation of China (Grant Nos. 12262001, 51869001, and 52268052). This research also was supported by the Key Laboratory of the Ministry of Education for Geomechanics and Embankment Engineering, Hohai University (Grant No. 2020008), and the Natural Science Foundation of the Jiangsu Province Higher Education Institutions of China (Grant No. 23KJB410001). The insightful comments and suggestions from the anonymous reviewers and the editor are also sincerely appreciated.
References
Azevedo, M. 2010. “Cylindrical excavations in soft soils supported by diaphragm walls.” [In Portuguese.] M.Sc. thesis, Dept. of Civil Engineering, Univ. of Porto.
Bang, S. 1985. “Active earth pressure behind retaining walls.” J. Geotech. Eng. 111 (3): 407–412. https://doi.org/10.1061/(ASCE)0733-9410(1985)111:3(407).
Benmebarek, S., A. Meftah, and N. Benmebarek. 2013. “Numerical study of the earth pressure distribution on cylindrical shafts.” In Proc., Int. Symp. on Innovative Technologies in Engineering and Science, 283–292. Turkey: Sakarya University Congress and Culture Center.
Berezantzev, V. G. 1958. “Earth pressure on the cylindrical retaining walls.” In Proc., Conf. on Earth Pressure Problem, 21–27. Brussels, Belgium: International Society of Soil Mechanics and Foundation Engineering, Belgian Group.
Borges, J. L., and G. T. Guerra. 2014. “Cylindrical excavations in clayey soils retained by jet grout walls: Numerical analysis and parametric study considering the influence of consolidation.” Comput. Geotech. 55: 42–56. https://doi.org/10.1016/j.compgeo.2013.07.008.
Brinkgreve, R. B. J., and W. Broere. 2006. Waterman, D. PLAXIS version 8.5 manual. Rotterdam, Netherlands: A.A. Balkema.
Cao, W., H. Zhang, T. Liu, and X. Tan. 2020. “Analytical solution for the active earth pressure of cohesionless soil behind an inclined retaining wall based on the curved thin-layer element method.” Comput. Geotech. 128: 103851. https://doi.org/10.1016/j.compgeo.2020.103851.
Chang, M.-F. 1997. “Lateral earth pressures behind rotating walls.” Can. Geotech. J. 34 (4): 498–509. https://doi.org/10.1139/t97-016.
Chehadeh, A., A. Turan, and F. Abed. 2015. “Numerical investigation of spatial aspects of soil structure interaction for secant pile wall circular shafts.” Comput. Geotech. 69: 452–461. https://doi.org/10.1016/j.compgeo.2015.06.014.
Chehadeh, A., A. Turan, F. Abed, and M. Yamin. 2019. “Lateral earth pressures acting on circular shafts considering soil-structure interaction.” Int. J. Geotech. Eng. 13 (2): 139–151. https://doi.org/10.1080/19386362.2017.1328081.
Cheng, Y. M., and Y. Y. Hu. 2005. “Active earth pressure on circular shaft lining obtained by simplified slip line solution with general tangential stress coefficient.” [In Chinese.] Chin. J. Geotech. Eng. 27 (1): 110–115.
Cheng, Y. M., Y. Y. Hu, and W. B. Wei. 2007. “General axisymmetric active earth pressure by method of characteristics—Theory and numerical formulation.” Int. J. Geomech. 7 (1): 1–15. https://doi.org/10.1061/(ASCE)1532-3641(2007)7:1(1).
Cho, J., H. Lim, S. Jeong, and K. Kim. 2015. “Analysis of lateral earth pressure on a vertical circular shaft considering the 3D arching effect.” Tunnelling Underground Space Technol. 48: 11–19. https://doi.org/10.1016/j.tust.2015.01.002.
Chun, B., and Y. Shin. 2006. “Active earth pressure acting on the cylindrical retaining wall of a shaft.” South Korea Ground Environ. Eng. J. 7 (4): 15–24.
Duan, S., X. Jiang, Q. Jiang, J. Xiong, and C. Li. 2023. “Theoretical solution and failure analysis of water pressure on lining of deep-buried non-circular hydraulic tunnel based on the equivalent hydraulic radius method.” Eng. Fail. Anal. 148: 107163. https://doi.org/10.1016/j.engfailanal.2023.107163.
Fan, X.-Z., C.-J. Xu, L.-J. Liang, Q.-Z. Chen, and J.-l. Deng. 2021. “Analytical solution for displacement-dependent passive earth pressure on rigid walls with various wall movements in cohesionless soil.” Comput. Geotech. 140: 104470. https://doi.org/10.1016/j.compgeo.2021.104470.
Fang, Y.-S., and I. Ishibashi. 1986. “Static earth pressures with various wall movements.” J. Geotech. Eng. 112 (3): 317–333. https://doi.org/10.1061/(ASCE)0733-9410(1986)112:3(317).
Fujii, T., T. Hagiwara, K. Ueno, and A. Taguchi. 1994. “Experiment and analysis of earth pressure on an axisymmetric shaft in sand.” In Proc., Int. Conf. on Centrifuge, 791–796. Fort Belvoir, VA: Defense Technical Information Centre.
Gao, Y. F., F. Zhang, G. H. Lei, and D. Y. Li. 2013. “An extended limit analysis of three-dimensional slope stability.” Géotechnique 63 (6): 518–524. https://doi.org/10.1680/geot.12.T.004.
He, W., C. Luo, J. Cui, and J. Zhang. 2017. “An axisymmetric BNEF method of circular excavations taking into account soil-structure interactions.” Comput. Geotech. 90: 155–163. https://doi.org/10.1016/j.compgeo.2017.06.001.
Herten, M., and M. Pulsfort. 1999. “Determination of spatial earth pressure on circular shaft constructions.” Granular Matter 2 (1): 1–7. https://doi.org/10.1007/s100350050028.
Kim, K.-Y., D.-S. Lee, J. Cho, S.-S. Jeong, and S. Lee. 2013. “The effect of arching pressure on a vertical circular shaft.” Tunnelling Underground Space Technol. 37: 10–21. https://doi.org/10.1016/j.tust.2013.03.001.
Konig, D., U. Guettler, and H. Jessberger. 1991. “Stress redistributions during tunnel and shaft constructions.” In Proc., Int. Conf. Centrifuge, 129–135. Rotterdam, The Netherlands: A.A. Balkema.
Lade, P., H. Jessberger, E. Makowski, and P. Jordan. 1981. “Modeling of deep shafts in centrifuge test.” In Proc., Int. Conf. on Soil Mechanics and Foundation Engineering, 683–691. Rotterdam, The Netherlands: A.A. Balkema.
Lim, A., P.-G. Hsieh, and C.-Y. Ou. 2016. “Evaluation of buttress wall shapes to limit movements induced by deep excavation.” Comput. Geotech. 78: 155–170. https://doi.org/10.1016/j.compgeo.2016.05.012.
Liu, F. Q. 2014. “Lateral earth pressures acting on circular retaining walls.” Int. J. Geomech. 14 (3): 04014002. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000291.
Liu, F. Q., and J. H. Wang. 2008. “A generalized slip line solution to the active earth pressure on circular retaining walls.” Comput. Geotech. 35 (2): 155–164. https://doi.org/10.1016/j.compgeo.2007.06.002.
Liu, F. Q., J. H. Wang, and L. L. Zhang. 2009. “Axi-symmetric active earth pressure obtained by the slip line method with a general tangential stress coefficient.” Comput. Geotech. 36 (1–2): 352–358. https://doi.org/10.1016/j.compgeo.2008.02.002.
Matsuzawa, H., and H. Hazarika. 1996. “Analyses of active earth pressure against rigid retaining wall subjected to different modes of movement.” Soils Found. 36 (3): 51–65. https://doi.org/10.3208/sandf.36.3_51.
Sabouni, R., and M. H. El Naggar. 2016. “Lateral earth pressure on cylindrical concrete shafts.” Geotech. Geol. Eng. 34 (4): 1199–1214. https://doi.org/10.1007/s10706-016-0039-1.
Schwamb, T., M. Elshafie, K. Soga, and R. Mail. 2016. “Considerations for monitoring of deep circular excavations.” ICE Proc. Geotech. Eng. 169: 1–17. https://doi.org/10.1680/jgeen.15.00063.
Schwamb, T., and K. Soga. 2015. “Numerical modelling of a deep circular excavation at Abbey Mills in London.” Géotechnique 65 (7): 604–619. https://doi.org/10.1680/geot.14.P.251.
Sherif, M. A., Y.-S. Fang, and R. I. Sherif. 1984. “KA and Ko behind rotating and Non-yielding walls.” J. Geotech. Eng. 110 (1): 41–56. https://doi.org/10.1061/(ASCE)0733-9410(1984)110:1(41).
Shu, S., B. Ge, Y. Wu, and F. Zhang. 2023. “Probabilistic assessment on 3D stability and failure mechanism of undrained slopes based on the kinematic approach of limit analysis.” Int. J. Geomech. 23 (1): 06022037. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002635.
Tan, Y., and D. Wang. 2015. “Structural behaviors of large underground earth-retaining systems in Shanghai. I: Unpropped circular diaphragm wall.” J. Perform. Constr. Facil 29 (2): 04014058. https://doi.org/10.1061/(ASCE)CF.1943-5509.0000521.
Terzaghi, K. 1943. Theoretical soil mechanics. New York: Wiley.
Tobar, T., and M. A. Meguid. 2010. “Comparative evaluation of methods to determine the earth pressure distribution on cylindrical shafts: A review.” Tunnelling Underground Space Technol. 25 (2): 188–197. https://doi.org/10.1016/j.tust.2009.11.001.
Tran, V. D. H., M. A. Meguid, and L. E. Chouinard. 2014. “Discrete element and experimental investigations of the earth pressure distribution on cylindrical shafts.” Int. J. Geomech. 14 (1): 80–91. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000277.
Paik, K. H., and R. Salgado. 2003. “Estimation of active earth pressure against rigid retaining walls considering arching effects.” Géotechnique 53 (7): 643–653. https://doi.org/10.1680/geot.2003.53.7.643.
Patel, S., and K. Deb. 2020. “Study of active earth pressure behind a vertical retaining wall subjected to rotation about the base.” Int. J. Geomech. 20 (4): 04020028. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001639.
Potts, D. M., and A. B. Fourie. 1984. “The behaviour of a propped retaining wall: Results of a numerical experiment.” Géotechnique 34 (3): 383–404. https://doi.org/10.1680/geot.1984.34.3.383.
Prater, E. G. 1977. “An examination of some theories of earth pressure on shaft linings.” Can. Geotech. J. 14 (1): 91–106. https://doi.org/10.1139/t77-007.
Qian, Z.-H., H.-Y. Shi, Q.-J. Pan, J.-F. Zou, and G.-H. Chen. 2021. “Active earth pressures on translating rigid walls against backfills with varying friction-angle distribution.” Int. J. Geomech. 21 (10): 06021024. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002118.
Waichita, S., P. Jongpradist, and P. Jamsawang. 2019. “Characterization of deep cement mixing wall behavior using wall-to-excavation shape factor.” Tunnelling Underground Space Technol. 83: 243–253. https://doi.org/10.1016/j.tust.2018.09.033.
Walz, B. 1973. “Left bracket apparatus for measuring the three-dimensional active soil pressure on a round model caisson right bracket.” [In German.] Baumaschine und Bautechnik. 20 (9): 339–344.
Wang, Y.-Z. 2000. “Distribution of earth pressure on a retaining wall.” Géotechnique 50 (1): 83–88. https://doi.org/10.1680/geot.2000.50.1.83.
Wong, R. C. K., and P. K. Kaiser. 1988. “Design and performance evaluation of vertical shafts: Rational shaft design method and verification of design method.” Can. Geotech. J. 25 (2): 320–337. https://doi.org/10.1139/t88-034.
Xie, M., J. Zheng, R. Zhang, L. Cui, and C. Miao. 2020. “Active earth pressure on rigid retaining walls built near rock faces.” Int. J. Geomech. 20 (6): 04020061. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001675.
Xu, R., B. Liao, J. Wu, and S. Chang. 2013. “Computational method for active earth pressure of cohesive soil under nonlimit state.” [In Chinese.] Rock Soil Mech. 34 (1): 148–154.
Zhang, F., B. Ge, D. Leshchinsky, S. Shu, and Y. Gao. 2023. “Effects of multitiered configuration on the internal stability of GRS walls.” J. Geotech. Geoenviron. Eng. 149 (12): 04023122. https://doi.org/10.1061/JGGEFK.GTENG-11723.
Zhang, J., M. Li, L. Ke, and J. Yi. 2022. “Distributions of lateral earth pressure behind rock-socketed circular diaphragm walls considering radial deflection.” Comput. Geotech. 143: 104604. https://doi.org/10.1016/j.compgeo.2021.104604.
Zhang, J.-M., Y. Shamoto, and K. Tokimatsu. 1998. “Evaluation of earth pressure under any lateral deformation.” Soils Found. 38 (1): 15–33. https://doi.org/10.3208/sandf.38.15.
Zhang, R., A. T. C. Goh, Y. Li, L. Hong, and W. Zhang. 2021. “Assessment of apparent earth pressure for braced excavations in anisotropic clay.” Acta Geotech. 16 (5): 1615–1626. https://doi.org/10.1007/s11440-020-01129-x.
Zhang, R., W. Zhang, and A. T. C. Goh. 2018. “Numerical investigation of pile responses caused by adjacent braced excavation in soft clays.” Int. J. Geotech. Eng. 15 (7): 783–797. https://doi.org/10.1080/19386362.2018.1515810.
Zhang, W., A. T. C. Goh, and F. Xuan. 2015. “A simple prediction model for wall deflection caused by braced excavation in clays.” Comput. Geotech. 63: 67–72. https://doi.org/10.1016/j.compgeo.2014.09.001.
Zhou, Y.-t., Q.-s. Chen, F.-q. Chen, X.-h. Xue, and S. Basack. 2018. “Active earth pressure on translating rigid retaining structures considering soil arching effect.” Eur. J. Environ. Civ. Eng. 22 (8): 910–926. https://doi.org/10.1080/19648189.2016.1229225.
Zhu, Y., F. Zhang, and S. Jia. 2022. “Embodied energy and carbon emissions analysis of geosynthetic reinforced soil structures.” J. Cleaner Prod. 370: 133510. https://doi.org/10.1016/j.jclepro.2022.133510.
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Published In
International Journal of Geomechanics
Volume 24 • Issue 5 • May 2024
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© 2024 American Society of Civil Engineers.
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Received: Jul 14, 2023
Accepted: Nov 12, 2023
Published online: Mar 13, 2024
Published in print: May 1, 2024
Discussion open until: Aug 13, 2024
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