Analytical prediction for lateral deformation of internal braced diaphragm wall in foundation pit based on plate theory

Abstract

Current analytical methods for predicting the lateral deformation of diaphragm walls require complex calculation processes, including numerous parameters with uncertain accuracy, which are difficult to use in practical engineering applications. In this study, we propose a novel analytical approach for calculating diaphragm wall deformation. First, a differential element moment balance method for calculating earth pressure is proposed using a simplified calculation. The excavation effect on the sliding wedge and multiple factors of the ground were considered. Subsequently, the work performed by the earth pressure and internal support structure was calculated. Based on plate theory, a calculation model for the diaphragm wall deformation was established, accounting for the interaction between the ground and internal support structure. Finally, the analytical model was solved using the principle of minimum potential energy and the Ritz method. The proposed method was validated by comparing field measurement data with numerical simulations. A parametric study was conducted to explore the sensitivities of the influencing factors on the lateral deformation of the diaphragm wall, from which a design scheme for the diaphragm wall was presented under the given deformation control standard.

Keywords

foundation pit / plate theory / analytical model / soil-structure interaction / internal braced diaphragm wall / Ritz method

References

[1] Han H-m, Shi B, Zhang Let al. . Deep displacement monitoring and foundation base boundary reconstruction analysis of diaphragm wall based on ultra-weak FBG [J]. Tunnelling and Underground Space Technology. 2021, 117: 104158.

[2] Zhang L-j, Cui Z-D. Effect of connection modes on seismic responses of a diaphragm wall-subway station system subjected to mainshock-aftershock sequences [J]. Soil Dynamics and Earthquake Engineering. 2024, 186108921.

[3] Teparaksa W, Teparaksa J. Comparison of diaphragm wall movement prediction and field performance for different construction techniques [J]. Underground Space. 2019, 4(3): 225-234.

[4] Xu Q-w, Xie J-l, Zhu H-het al. . Supporting behavior evolution of ultra-deep circular diaphragm walls during excavation: Monitoring and assessment methods comparison [J]. Tunnelling and Underground Space Technology. 2024, 143: 105495.

[5] Ou X-f, Liao W, Zheng X-cet al. . Large deformation problems arising from deep excavation in silt strata: A case study in Shenzhen, China [J]. Journal of Rock Mechanics and Geotechnical Engineering. 2025, 1742576-2589.

[6] Chen C, Zhan L-t, Chen G-net al. . Bayesian updating of time-dependent diaphragm wall deflections in deep excavations in soft soils using different datasets [J]. Computers and Geotechnics. 2024, 173: 106499.

[7] Li Y j, Zhou Z-w, Alcalá Jet al. . Research on spatial deformation monitoring and numerical coupling of deep foundation pit in soft soil [J]. Journal of Building Engineering. 2025, 99111636.

[8] Xu Z-h, Wang J-h, Wang W-D. Deformation behavior of diaphragm walls in deep excavations in Shanghai [J]. China Civil Engineering Journal. 2008, 881-86(in Chinese)

[9] Hou Y M, Wang J H, Zhang L L. Finite-element modeling of a complex deep excavation in Shanghai [J]. Acta Geotechnica. 2009, 417-16.

[10] Wang L, Zheng G, Ou R-N. Differential uplift and settlement between inner column and diaphragm wall in top-down excavation [J]. Journal of Central South University. 2015, 22(9): 3578-3590.

[11] Wu G-j, Chen W-z, Bian H-bet al. . Structure optimisation of a diaphragm wall with special modelling methods in a large-scale circular ventilating shaft considering shield crossing [J]. Tunnelling and Underground Space Technology. 2017, 65: 35-41.

[12] Bahrami M, Khodakarami M I, Haddad A. 3D numerical investigation of the effect of wall penetration depth on excavations behavior in sand [J]. Computers and Geotechnics. 2018, 98: 82-92.

[13] Zhang J, Xie R, Zhang H. Mechanical response analysis of the buried pipeline due to adjacent foundation pit excavation [J]. Tunnelling and Underground Space Technology. 2018, 78: 135-145.

[14] Zhuang H-y, Wang R, Shi P-xet al. . Seismic response and damage analysis of underground structures considering the effect of concrete diaphragm wall [J]. Soil Dynamics and Earthquake Engineering. 2019, 116: 278-288.

[15] Ye S-h, Zhao Z-f, Wang D. Deformation analysis and safety assessment of existing metro tunnels affected by excavation of a foundation pit [J]. Underground Space. 2021, 6(4): 421-431.

[16] Yong W-x, Zhang W-g, Nguyen Het al. . Analysis and prediction of diaphragm wall deflection induced by deep braced excavations using finite element method and artificial neural network optimized by metaheuristic algorithms [J]. Reliability Engineering & System Safety. 2022, 221: 108335.

[17] Osman A S, Bolton M D. A new design method for retaining walls in clay [J]. Canadian Geotechnical Journal. 2004, 41(3): 451-466.

[18] Liu M-l, Fang Q, Zhang D-let al. . Prediction of transient deformation due to excavation based on improved MSD method [J]. Chinese Journal of Rock Mechanics and Engineering. 2018, 3771700-1707(in Chinese)

[19] Saleh M, Vanapalli S K. Analysis of excavation support systems considering the influence of saturated and unsaturated soil conditions [J]. Journal of Geotechnical and Geoenvironmental Engineering. 2022, 148(6): 04022034.

[20] Elchiti I, Saad G, Najjar SS. Passive p-y curves for rigid basement walls supporting granular soils [J]. Geomechanics And Engineering. 2023, 323335-346

[21] Cui X-y, Li Z-p, He H-fet al. . Improved calculation method for corresponding characteristics of foundation pit excavation on the diaphragm wall [J]. Alexandria Engineering Journal. 2024, 103: 251-265.

[22] Conte E, Troncone A. Simplified analysis of cantilever diaphragm walls in cohesive soils [J]. Soils and Foundations. 2018, 58(6): 1446-1457.

[23] Crispin J J, Bateman A H, Voyagaki Eet al. . MSD applied to the construction of the British Library basement: A multi-stage excavation in London Clay [J]. Canadian Geotechnical Journal. 2024, 61(3): 596-603.

[24] Li E-b, Tan Y-h, Zhang S-get al. . Analytic calculation of deformation of diaphragm wall for conserving deep foundation pit [J]. Journal of PLA University of Science and Technology. 2004, 5(2): 57-60(in Chinese)

[25] Ou Q, Zhang L, Zhao M-het al. . Lateral displacement and internal force in diaphragm walls based on principle of minimum potential energy [J]. International Journal of Geomechanics. 2019, 19(6): 04019055.

[26] Tong L H, Lin F, Xiang Yet al. . Buckling analysis of nanoplates based on a generic third-order plate theory with shear-dependent non-isotropic surface stresses [J]. Composite Structures. 2021, 265: 113708.

[27] Tong L H, Guo W-l, Xu C-jet al. . Simplified theoretical prediction for lateral deformation of a diaphragm wall using the general third-order plate theory [J]. International Journal of Geomechanics. 2023, 231104023188.

[28] RANKINE W J M. II. On the stability of loose earth [J]. Philosophical Transactions of the Royal Society of London, 1857(147): 9–27. DOI:https://doi.org/10.1098/rstl.1857.0003.

[29] Coulomb C A. Essay on an application of the rules of maxima and minima to some statics problems relevant to architecture [J]. Memoire Académie Royale des Sciences, Paris. 1776, 7343-382

[30] Chen B-g, Yan T-f, Song D-bet al. . Experimental investigations on a deep excavation support system with adjustable strut length [J]. Tunnelling and Underground Space Technology. 2021, 115: 104046.

[31] Jiang J, Fu C-z, Wang S-wet al. . An analytical p-y curve method based on compressive soil pressure model in sand soil [J]. Journal of Central South University. 2022, 2961987-2004.

[32] Bao N, Chen J-f, Wang G-het al. . Analytical prediction of displacement-dependent lateral earth pressure against stabilizing piles in sandy slopes considering arching effect [J]. Computers and Geotechnics. 2024, 176: 106776.

[33] Liu J-f, Cao H-y, Wang Y-qet al. . Analytical solution of active earth pressure considering soil arching for cohesive soil [J]. Journal of Railway Science and Engineering. 2023, 20124604-4612(in Chinese)

[34] Lin Z-r, Jiang Y-l, Xiong Yet al. . Analytical solution for displacement-dependent active earth pressure considering the stiffness of cantilever retaining structure in cohesionless soil [J]. Computers and Geotechnics. 2024, 170: 106258.

[35] Nguyen T. An exact solution of active earth pressures based on a statically admissible stress field [J]. Computers and Geotechnics. 2023, 153105066.

[36] Zhou Y-y, Ren M-L. Experimental study of active earth pressure in rigid retaining walls [J]. Chinese Journal of Geotechnical Engineering. 1990, 12219-26(in Chinese)

[37] Han M, Chen X-s, Li Zet al. . Improved inverse analysis methods and modified apparent earth pressure for braced excavations in soft clay [J]. Computers and Geotechnics. 2023, 159: 105456.

[38] Gogolik S, Kopras M, Szymczak-Graczyk Aet al. . Experimental evaluation of the size and distribution of lateral pressure on the walls of the excavation support [J]. Journal of Building Engineering. 2023, 73106831.

[39] Zhang J-w, Li M-d, Yi J-xet al. . Analytical solution for radial displacement–dependent earth pressure acting on underwater rock-socketed circular diaphragm walls [J]. International Journal of Geomechanics. 2024, 24504024083.

[40] Fu H-l, Wang C-y, Li H. Active earth pressure for subgrade retaining walls in cohesive backfills with tensile strength cut-off subjected to seepage effects [J]. Journal of Central South University. 2020, 2772148-2159.

[41] Liu Z-y, Chen J. Active earth pressure against rigid retaining wall considering shear stress under translation mode [J]. Chinese Journal of Geotechnical Engineering. 2016, 38122254-2261(in Chinese)

[42] Zienkiewicz O C, Taylor R L, Govindjee S. Plate bending approximation: Thin and thick plates [M]. The Finite Element Method. 2025, Amsterdam, Elsevier429488.

[43] Zienkiewicz O C, Taylor R L, Zhu J Z. Plate bending approximation: Thin and thick plates [M]. The Finite Element Method: its Basis and Fundamentals. 2013, Amsterdam, Elsevier407466.

[44] Belardi V G, Fanelli P, Vivio F. Application of the Ritz method for the bending and stress analysis of thin rectilinear orthotropic composite sector plates [J]. Thin-Walled Structures. 2023, 183: 110374.

[45] Jing Z, Duan L. Discrete Ritz method for buckling analysis of arbitrarily shaped plates with arbitrary cutouts [J]. Thin-Walled Structures. 2023, 193111294.

[46] Feng G-h, Xu C-j, Ding Zet al. . Enhanced theoretical approach for predicting the tunnel response due to deep excavation above [J]. Transportation Geotechnics. 2024, 48101309.

[47] Xu Z-h, Wang W-D. Selection of soil constitutive models for numerical analysis of deep excavations in close proximity to sensitive properties [J]. Rock and Soil Mechanics. 2010, 31(1): 258-264326. (in Chinese)

[48] Woo S M, Moh Z C. Geotechnical characteristics of soils in the Taipei Basin [R]. Southeast Asian Geotechnical Conference, Taipei, China. 199051-63

[49] Wang X, Pan Y, Li M-get al. . Determining and estimating the fracture risk of diaphragm wall from observed lateral deflection [M]. Proceedings of the 2022 International Conference on Green Building, Civil Engineering and Smart City. 2022, Singapore, Springer Nature Singapore884892

[50] Bilotta E. Use of diaphragm walls to mitigate ground movements induced by tunnelling [J]. Géotechnique. 2008, 58(2): 143-155.

[51] Hariri-Ardebili M A, Segura C L, Sattar S. Probabilistic sensitivity matrices under stressor uncertainty [J]. Soil Dynamics and Earthquake Engineering. 2024, 179108551.

[52] China Architecture & Building Press. Technical specification for retaining and protection of building foundation excavations [Z]. 2012(JGJ 120-2012)

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