Technical Papers
Aug 17, 2023

Simplified Theoretical Prediction for Lateral Deformation of a Diaphragm Wall Using the General Third-Order Plate Theory

Publication: International Journal of Geomechanics
Volume 23, Issue 11

Abstract

The diaphragm wall is widely used in deep excavation engineering to guarantee the safety of the foundation pit and surrounding environment during excavation. An accurate prediction of the lateral deformation of the diaphragm wall is the basis of the design and optimization of the diaphragm wall structure. In this paper, we apply the third-order shear deformation plate theory to develop an analytical method for predicting the lateral deformation of the diaphragm wall to take into account the effects of shear stress distributed along the thickness direction on the lateral deformation. By using the Pb-2 Ritz method, combined with the minimum potential energy concept, the analytical solution for the deformation of the diaphragm wall is obtained under certain simplifications. Three types of boundary conditions for the bottom side of the diaphragm wall are considered to meet different geological conditions. The proposed method is verified by comparing the results predicted in this study with the monitoring data obtained from the practical pit engineering of Dinggong south road metro station of Metro Line 2 in Nanchang, Jiangxi province, China. Finally, the effects of the thickness and the embedded depth of the diaphragm wall and the lateral support patterns are analyzed, and the optimized design parameters for the diaphragm wall are also suggested. The proposed method can theoretically provide preliminary parameter optimization guidance for the design and construction of a diaphragm wall.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

This work was supported by the National Natural Science Fund (52278350, 52208344, 52168049, and 52238009) and the Natural Science Foundation of Jiangxi Province (20212BDH81034).

References

Amabili, M., and J. N. Reddy. 2020. “The nonlinear, third-order thickness and shear deformation theory for statics and dynamics of laminated composite shells.” Compos. Struct. 244: 112265. https://doi.org/10.1016/j.compstruct.2020.112265.
Arai, Y., O. Kusakabe, O. Murata, and S. Konishi. 2008. “A numerical study on ground displacement and stress during and after the installation of deep circular diaphragm walls and soil excavation.” Comput. Geotech. 35 (5): 791–807. https://doi.org/10.1016/j.compgeo.2007.11.001.
Azzam, W. R., and A. Z. Elwakil. 2017. “Performance of axially loaded-piled retaining wall: Experimental and numerical analysis.” Int. J. Geomech. 17 (2): 04016049. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000710.
Bacciocchi, M., and A. M. Tarantino. 2021. “Third-order theory for the bending analysis of laminated thin and thick plates including the strain gradient effect.” Materials 14 (7): 1771. https://doi.org/10.3390/ma14071771.
Bilotta, E. 2008. “Use of diaphragm walls to mitigate ground movements induced by tunnelling.” Géotechnique 58 (2): 143–155. https://doi.org/10.1680/geot.2008.58.2.143.
CGS (Canadian Geotechnical Society). 2006. Canadian foundation engineering manual. 4th ed. Richmond, BC: CGS.
Chowdhury, S. S., K. Deb, and A. Sengupta. 2013. “Estimation of design parameters for braced excavation: Numerical study.” Int. J. Geomech. 13 (3): 234–247. https://doi.org/10.1007/s10706-016-0123-6.
Conte, E., and A. Troncone. 2018. “Simplified analysis of cantilever diaphragm walls in cohesive soils.” Soils Found. 58 (6): 1446–1457. https://doi.org/10.1016/j.sandf.2018.08.012.
Finno, R. J., F. T. Voss, E. Rossow, and J. T. Blackburn. 2005. “Evaluating damage potential in buildings affected by excavations.” J. Geotech. Geoenviron. Eng. 131 (10): 1199–1210. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:10(1199).
GB (Guobiao Standards). 2015. Code for design of concrete structures. GB 50010-2010. Beijing: GB.
Hsieh, Y.-M., P. H. Dang, and H.-D. Lin. 2017. “How small strain stiffness and yield surface affect undrained excavation predictions.” Int. J. Geomech. 17 (3): 04016071. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000753.
Hsiung, B.-C. B. 2009. “A case study on the behaviour of a deep excavation in sand.” Comput. Geotech. 36 (4): 665–675. https://doi.org/10.1016/j.compgeo.2008.10.003.
James, A., and B. Kurian. 2022. “Diaphragm wall retaining system—A simplified model for design loads.” Aust. J. Civil Eng. 20: 374–388. https://doi.org/10.1080/14488353.2021.1991549.
Kim, J., and J. N. Reddy. 2013. “Analytical solutions for bending, vibration, and buckling of FGM plates using a couple stress-based third-order theory.” Compos. Struct. 103: 86–98. https://doi.org/10.1016/j.compstruct.2013.03.007.
Kung, G. T., C. H. Juang, E. C. Hsiao, and Y. M. Hashash. 2007. “Simplified model for wall deflection and ground-surface settlement caused by braced excavation in clays.” J. Geotech. Geoenviron. Eng. 133 (6): 731–747. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:6(731).
Liew, K. M., and C. M. Wang. 1992. “Elastic buckling of rectangular plates with curved internal supports.” J. Struct. Eng. 118 (6): 1480–1493. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:6(1480).
Liew, K. M., and C. M. Wang. 1993. “pb-2 Rayleigh–Ritz method for general plate analysis.” Eng. Struct. 15 (1): 55–60. https://doi.org/10.1016/0141-0296(93)90017-X.
Liu, W., P. Shi, G. Cai, and C. Cao. 2021. “Seepage on local stability of slurry trench in deep excavation of diaphragm wall construction.” Comput. Geotech. 129: 103878. https://doi.org/10.1016/j.compgeo.2020.103878.
Mohamed, A. Z. 2017. Effect of diaphragm wall construction on adjacent deep foundation. Freiberg, Germany: Technische Universitat Bergakademie.
Ng, C. W. W., and G. H. Lei. 2003. “An explicit analytical solution for calculating horizontal stress changes and displacements around an excavated diaphragm wall panel.” Can. Geotech. J. 40 (4): 780–792. https://doi.org/10.1139/t03-027.
Ooi, P. S. K., and T. L. Ramsey. 2003. “Curvature and bending moments from inclinometer data.” Int. J. Geomech. 3 (1): 64–74. https://doi.org/10.1061/(ASCE)1532-3641(2003)3:1(64).
Ou, Q., L. Zhang, M. Zhao, and Y. Wang. 2019. “Lateral displacement and internal force in diaphragm walls based on principle of minimum potential energy.” Int. J. Geomech. 19 (6): 04019055. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001415.
Parsa-Pajouh, A., B. Fatahi, and H. Khabbaz. 2016. “Experimental and numerical investigations to evaluate two-dimensional modeling of vertical drain-assisted preloading.” Int. J. Geomech. 16 (1): B4015003. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000507.
Reddy, J. N. 1984a. “A refined nonlinear theory of plates with transverse shear deformation.” Int. J. Solids Struct. 20 (9): 881–896. https://doi.org/10.1016/0020-7683(84)90056-8.
Reddy, J. N. 1984b. “A simple higher-order theory for laminated composite plates.” J. Appl. Mech. 51 (4): 745–752. https://doi.org/10.1115/1.3167719.
Segura-Castillo, L., A. Aguado, and A. Josa. 2013. “Bi-layer diaphragm walls: Experimental and numerical structural analysis.” Eng. Struct. 56: 154–164. https://doi.org/10.1016/j.engstruct.2013.04.018.
Spagnoli, G., P. Oreste, and L. Lo Bianco. 2017. “Estimation of shaft radial displacement beyond the excavation bottom before installation of permanent lining in nondilatant weak rocks with a novel formulation.” Int. J. Geomech. 17 (12): 04017051. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000949.
Tong, L. H., F. Lin, Y. Xiang, H.-S. Shen, and C. W. Lim. 2021. “Buckling analysis of nanoplates based on a generic third-order plate theory with shear-dependent non-isotropic surface stresses.” Compos. Struct. 265: 113708. https://doi.org/10.1016/j.compstruct.2021.113708.
Wang, C. M., K. M. Liew, Y. Xiang, and S. Kitipornchai. 1993. “Buckling of rectangular mindlin plates with internal line supports.” Int. J. Solids Struct. 30 (1): 1–17. https://doi.org/10.1016/0020-7683(93)90129-U.
Wang, J. H., Z. H. Xu, and W. D. Wang. 2010. “Wall and ground movements due to deep excavations in Shanghai soft soils.” J. Geotech. Geoenviron. Eng. 136 (7): 985–994. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000299.
Wang, W., Y. Lu, D. Zhao, J. Zhang, and X. Bai. 2020. “Research on large deflection deformation reconstruction of elastic thin plate based on strain monitoring.” Measurement 149: 107000. https://doi.org/10.1016/j.measurement.2019.107000.
Wang, Y. X., P. P. Guo, W. X. Ren, B. X. Yuan, H. P. Yuan, Y. L. Zhao, S. B. Shan, and P. Cao. 2017. “Laboratory investigation on strength characteristics of expansive soil treated with jute fiber reinforcement.” J. Vib. Acoust. 17 (11): 04017101.
Wei, G., P. Lardeur, and F. Druesne. 2022. “Solid-shell approach based on first-order or higher-order plate and shell theories for the finite element analysis of thin to very thick structures.” Eur. J. Mech. A. Solids 94: 104591. https://doi.org/10.1016/j.euromechsol.2022.104591.
Wu, J.-j., Q.-g. Cheng, H. Wen, L.-j. Wang, Y. Li, and J.-l. Zhang. 2016. “A load transfer approach to rectangular closed diaphragm walls.” Proc. Inst. Civ. Eng. Geotech. Eng. 169 (6): 509–526. https://doi.org/10.1680/jgeen.15.00156.
Yan, J. W., L. H. Tong, C. Li, Y. Zhu, and Z. W. Wang. 2015. “Exact solutions of bending deflections for nano-beams and nano-plates based on nonlocal elasticity theory.” Compos. Struct. 125: 304–313. https://doi.org/10.1016/j.compstruct.2015.02.017.
Yoo, C. S., B. S. Choi, and H. Y. Jung. 2006. “Excavation-induced buried pipeline failure—A case study.” Solid State Phenom. 110: 23–30. https://doi.org/10.4028/www.scientific.net/SSP.110.23.
Yoo, C., and D. Lee. 2008. “Deep excavation-induced ground surface movement characteristics—A numerical investigation.” Comput. Geotech. 35 (2): 231–252. https://doi.org/10.1016/j.compgeo.2007.05.002.
Zhao, C. 2009. Dynamic and transient infinite elements: Theory and geophysical, geotechnical and geoenvironmental applications. Berlin: Springer.
Zhao, C. 2014. Physical and chemical dissolution front instability in porous media: Theoretical analyses and computational simulations. Heidelberg, Germany: Springer.
Zhao, C., B. E. Hobbs, and A. Ord. 2008. Convective and advective heat transfer in geological systems. Berlin: Springer.
Zhao, C., B. E. Hobbs, and A. Ord. 2009. Fundamentals of computational geoscience: Numerical methods and algorithms. Berlin: Springer.
Zhao, C., B. E. Hobbs, and A. Ord. 2010a. “Theoretical analyses of the effects of solute dispersion on chemical-dissolution front instability in fluid-saturated porous media.” Transp. Porous Media 84: 629–653. https://doi.org/10.1007/s11242-010-9528-5.
Zhao, C., B. E. Hobbs, and A. Ord. 2010b. “Theoretical analyses of nonaqueous-phase-liquid dissolution induced instability in two-dimensional fluid-saturated porous media.” Int. J. Numer. Anal. Methods Geomech. 34: 1767–1796. https://doi.org/10.1002/nag.880.
Zhao, C., B. E. Hobbs, and A. Ord. 2013a. “Analytical solutions of nonaqueous-phase-liquid dissolution problems associated with radial flow in fluid-saturated porous media.” J. Hydrol. 494: 96–106. https://doi.org/10.1016/j.jhydrol.2013.04.038.
Zhao, C., B. E. Hobbs, and A. Ord. 2013b. “Theoretical analyses of acidization-dissolution front instability in fluid-saturated carbonate rocks.” Int. J. Numer. Anal. Methods Geomech. 37: 2084–2105. https://doi.org/10.1002/nag.2123.
Zhao, C., B. E. Hobbs, and A. Ord. 2015a. “Theoretical analyses of chemical dissolution-front instability in fluid-saturated porous media under non-isothermal conditions.” Int. J. Numer. Anal. Methods Geomech. 39: 799–820. https://doi.org/10.1002/nag.2332.
Zhao, C., T. Poulet, and K. Regenauer-Lieb. 2015b. “Numerical modeling of toxic nonaqueous phase liquid removal from contaminated groundwater systems: Mesh effect and discretization error estimation.” Int. J. Numer. Anal. Methods Geomech. 39: 571–593. https://doi.org/10.1002/nag.2327.
Zhao, C., B. E. Hobbs, and A. Ord. 2016. “Chemical dissolution-front instability associated with water–rock reactions in groundwater hydrology: Analyses of porosity–permeability relationship effects.” J. Hydrol. 540: 1078–1087. https://doi.org/10.1016/j.jhydrol.2016.07.022.
Zhao, C. B., B. Hobbs, and A. Ord. 2017. “A new alternative approach for investigating acidization dissolution front propagation in fluid-saturated rocks.” Sci. China Technol. Sci. 60: 1197–1210. https://doi.org/10.1007/s11431-016-0666-1.
Zhao, C., B. E. Hobbs, P. Hornby, A. Ord, S. Peng, and L. Liu. 2008a. “Theoretical and numerical analyses of chemical-dissolution front instability in fluid-saturated porous rocks.” Int. J. Numer. Anal. Methods Geomech. 32: 1107–1130. https://doi.org/10.1002/nag.661.
Zhao, C., B. E. Hobbs, and A. Ord. 2018b. “Analytical solution for dissolution-timescale reactive transport in fluid-saturated porous rocks.” Int. J. Geomech. 18 (6): 1–10. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001152.
Zhao, C., B. E. Hobbs, and A. Ord. 2020. “Transient-state instability analysis of dissolution-timescale reactive infiltration in fluid-saturated porous rocks: Purely mathematical approach.” Sci. China Technol. Sci. 63: 319–328. https://doi.org/10.1007/s11431-018-9448-8.
Zhao, C., B. E. Hobbs, and A. Ord. 2022. “Two different mathematical schemes for solving chemical dissolution-front instability problems in fluid-saturated rocks.” Sci. China Technol. Sci. 65: 147–156. https://doi.org/10.1007/s11242-022-01851-y.
Zheng, Y., Z.-W. Zhu, Q.-X. Deng, and F. Xiao. 2019. “Theoretical and experimental study on the fiber Bragg grating-based inclinometer for slope displacement monitoring.” Opt. Fiber Technol. 49: 28–36. https://doi.org/10.1016/j.yofte.2019.01.031.

Information & Authors

Information

Published In

Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 23Issue 11November 2023

History

Received: Oct 31, 2022
Accepted: May 8, 2023
Published online: Aug 17, 2023
Published in print: Nov 1, 2023
Discussion open until: Jan 17, 2024

Permissions

Request permissions for this article.

Authors

Affiliations

State Key Laboratory of Performance Monitoring and Guarantee of Rail Transportation Infrastructure, Nanchang 330013, Jiangxi, China; Institute of Geotechnical Engineering, School of Civil Engineering and Architecture, East China Jiaotong Univ., Nanchang 330013, Jiangxi, China. Email: [email protected]
Wanglong Guo [email protected]
State Key Laboratory of Performance Monitoring and Guarantee of Rail Transportation Infrastructure, Nanchang 330013, Jiangxi, China; Institute of Geotechnical Engineering, School of Civil Engineering and Architecture, East China Jiaotong Univ., Nanchang 330013, Jiangxi, China. Email: [email protected]
Changjie Xu [email protected]
State Key Laboratory of Performance Monitoring and Guarantee of Rail Transportation Infrastructure, Nanchang 330013, Jiangxi, China; Institute of Geotechnical Engineering, School of Civil Engineering and Architecture, East China Jiaotong Univ., Nanchang 330013, Jiangxi, China. Email: [email protected]
State Key Laboratory of Performance Monitoring and Guarantee of Rail Transportation Infrastructure, Nanchang 330013, Jiangxi, China; Institute of Geotechnical Engineering, School of Civil Engineering and Architecture, East China Jiaotong Univ., Nanchang 330013, Jiangxi, China (corresponding author). ORCID: https://orcid.org/0000-0002-8140-4263. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share