Abstract
Determinations of active earth pressures are commonly performed two-dimensionally (2D) based on completely saturated and/or dry assumptions, though the soil in cases of geotechnical interest is mostly unsaturated and the earth pressures are usually of conspicuous three-dimensional (3D) features. In this paper, a novel finite prismoid element method (FPEM) for calculating the lateral earth pressures acting against the retaining wall is suggested. The main feature of the FPEM is that the whole backfill is discretized into numerous horizontally distributed prismoid elements that might characterized with different soil properties. For unsaturated backfills, the prismoid elements are characterized with various soil cohesions and unit soil weights. Upper bound solutions to active earth pressures under 2D and 3D conditions with and without suction are both calculated and compared with several other analytical ones, indicating the reliability and applicability of the proposed method. The responses of unsaturated backfills to surcharge loads on the crest are numerically studied and discussed. An illustrative example is reexamined to further demonstrate the practical use of the technique.
Similar content being viewed by others
References
Abdollahi M, Vahedifard F, Abed M, Leshchinsky BA (2021) Effect of tension crack formation on active earth pressure encountered in unsaturated retaining wall backfills. Journal of Geotechnical and Geoenvironmental Engineering 147(2):06020028, DOI: https://doi.org/10.1061/(ASCE)GT.1943-5606.0002434
Al-Homoud AS, Whitman RV (1995) Comparison between fe prediction and results from dynamic centrifuge tests on tilting gravity walls. Soil Dynamics and Earthquake Engineering 14(4):259–268, DOI: https://doi.org/10.1016/0267-7261(94)00051-h
Antão AN, Santana TG, Da Silva MV, Guerra NMC (2016) Three-dimensional active earth pressure coefficients by upper bound numerical limit analysis. Computers and Geotechnics 79:96–104, DOI: https://doi.org/10.1016/j.compgeo.2016.05.022
Cao WG, Liu T, Xu Z (2019) Estimation of active earth pressure on inclined retaining wall based on simplified principal stress trajectory method. International Journal of Geomechanics 19(7):06019011, DOI: https://doi.org/10.1061/(ASCE)gm.1943-5622.0001447
Drucker DC, Prager W (1952) Soil mechanics and plastic analysis or limit design. Quarterly of Applied Mathematics 10(2):157–165, DOI: https://doi.org/10.1090/qam/48291
Fathipour H, Payan M, Chenari RJ (2021) Limit analysis of lateral earth pressure on geosynthetic-reinforced retaining structures using finite element and second-order cone programming. Computers and Geotechnics 134:104119, DOI: https://doi.org/10.1016/j.compgeo.2021.104119
Fathipour H, Siahmazgi SA, Payan M, Chenari RJ (2020) Evaluation of the lateral earth pressure in unsaturated soils with finite element limit analysis using second-order cone programming. Computers and Geotechnics 125:103587, DOI: https://doi.org/10.1016/j.compgeo.2020.103587
Gao Y, Li Z, Sun DA, Yu HH (2021) A simple method for predicting the hydraulic properties of unsaturated soils with different void ratios. Soil and Tillage Research 209:104913, DOI: https://doi.org/10.1016/j.still.2020.104913
Griffiths DV, Lu N (2005) Unsaturated slope stability analysis with steady infiltration or evaporation using elasto-plastic finite elements. International Journal for Numerical and Analytical Methods in Geomechanics 29(3):249–267, DOI: https://doi.org/10.1002/nag.413
Hettler A, Kurrer K-E (2019) Earth pressure. Wilhelm Ernst & Sohn, Berlin, Germany
Huang WX, Sun DA, Sloan SW (2007) Analysis of the failure mode and softening behaviour of sands in true triaxial tests. International Journal of Solids and Structures 44(5):1423–1437, DOI: https://doi.org/10.1016/j.ijsolstr.2006.06.026
Jin XF, Liang ST, Zhu XJ (2015) Stability of three-dimensional slurry trenches with inclined ground surface: A theoretical study. Advances in Materials Science and Engineering 2015:362160, DOI: https://doi.org/10.1155/2015/362160
Jo SB, Ha JG, Lee JS, Kim DS (2017) Evaluation of the seismic earth pressure for inverted T-shape stiff retaining wall in cohesionless soils via dynamic centrifuge. Soil Dynamics and Earthquake Engineering 92:345–357, DOI: https://doi.org/10.1016/j.soildyn.2016.10.009
Kim WS, Borden RH (2013) Numerical simulation of MSE wall behavior induced by surface-water infiltration. Journal of Geotechnical and Geoenvironmental Engineering 139(12):2110–2124, DOI: https://doi.org/10.1061/(ASCE)gt.1943-5606.0000927
Li MG, Chen JJ, Wang JH (2017) Arching effect on lateral pressure of confined granular material: Numerical and theoretical analysis. Granular Matter 19(2):20, DOI: https://doi.org/10.1007/s10035-017-0700-2
Li XG, Liu WN (2010) Study on the action of the active earth pressure by variational limit equilibrium method. International Journal for Numerical and Analytical Methods in Geomechanics 34:991–1008, DOI: https://doi.org/10.1002/nag.840
Likos WJ, Lu N, Godt JW (2014) Hysteresis and uncertainty in soil water-retention curve parameters. Journal of Geotechnical and Geoenvironmental Engineering 140(4):04013050, DOI: https://doi.org/10.1061/(ASCE)GT.1943-5606.0001071
Lu N, Godt JW, Wu DT (2010) A closed-form equation for effective stress in unsaturated soil. Water Resources Research 46(5):W05515, DOI: https://doi.org/10.1029/2009WR008646
Lu N, Griffiths DV (2004) Profiles of steady-state suction stress in unsaturated soils. Journal of Geotechnical and Geoenvironmental Engineering 130(10):1063–1076, DOI: https://doi.org/10.1061/(ASCE)1090-0241(2004)130:10(1063)
Michalowski RL, Drescher A (2009) Three-dimensional stability of slopes and excavations. Géotechnique 59(10):839–850, DOI: https://doi.org/10.1680/geot.8.P.136
Park BS, Lee J, Kim SC, Lee SD (2018) Investigation of three-dimensional active earth pressure and load transfer according to aspect ratio. Marine Georesources and Geotechnology 37(3):322–330, DOI: https://doi.org/10.1080/1064119X.2017.1420715
Patel S, Deb K (2020) Study of active earth pressure behind a vertical retaining wall subjected to rotation about the base. International Journal of Geomechanics 20(4):04020028, DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0001639
Santos PJ, Barros PLA (2015) Active earth pressure due to soil mass partially subjected to water seepage. Canadian Geotechnical Journal 52(11):1886–1891, DOI: https://doi.org/10.1139/cgj-2014-0367
Sloan SW (2013) Geotechnical stability analysis. Géotechnique 63(7):531–572, DOI: https://doi.org/10.1680/geot.12.RL.001
Soubra AH, Regenass P (2000) Three-dimensional passive earth pressures by kinematical approach. Journal of Geotechnical and Geoenvironmental Engineering 126(11):969–978, DOI: https://doi.org/10.1061/(ASCE)1090-0241(2000)126:11(969)
Tom Wörden F, Achmus M (2013) Numerical modeling of three-dimensional active earth pressure acting on rigid walls. Computers and Geotechnics 51:83–90, DOI: https://doi.org/10.1016/j.compgeo.2013.02.004
Vahedifard F, Leshchinsky BA, Mortezaei K, Lu N (2015) Active earth pressures for unsaturated retaining structures. Journal of Geotechnical and Geoenvironmental Engineering 141(11):04015048, DOI: https://doi.org/10.1061/(ASCE)gt.1943-5606.0001356
van Genuchten MT (1980) A closed-form equation predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44(5):892–898, DOI: https://doi.org/10.2136/sssaj1980.03615995004400050002x
Veiskarami M, Jamshidi Chenari R, Jameei AA (2019) A study on the static and seismic earth pressure problems in anisotropic granular media. Geotechnical and Geological Engineering 37(3):1987–2005, DOI: https://doi.org/10.1007/s10706-018-0739-9
Wang L, Hu W, Sun DA, Li L (2019) 3D stability of unsaturated soil slopes with tension cracks under steady infiltrations. International Journal for Numerical and Analytical Methods in Geomechanics 43(6):1184–1206, DOI: https://doi.org/10.1002/nag.2889
Wang L, Liu WH, Hu W, Li WG, Sun DA (2021) Effects of seismic force and pore-water pressure on stability of 3D unsaturated hillslopes. Natural Hazards 105(2):2093–2116, DOI: https://doi.org/10.1007/s11069-020-04391-0
Wang L, Sun DA, Yao YP, Wu LZ, Xu YF (2020) Kinematic limit analysis of three-dimensional unsaturated soil slopes reinforced with a row of piles. Computers and Geotechnics 120:103428, DOI: https://doi.org/10.1016/j.compgeo.2019.103428
Xiong GJ, Wang JH, Chen JJ (2019) Theory and practical calculation method for axisymmetric active earth pressure based on the characteristics method considering the compatibility condition. Applied Mathematical Modelling 68:563–582, DOI: https://doi.org/10.1016/j.apm.2018.11.022
Yang XL, Li ZW (2018) Upper bound analysis of 3D static and seismic active earth pressure. Soil Dynamics and Earthquake Engineering 108:18–28, DOI: https://doi.org/10.1016/j.soildyn.2018.02.006
Yang CW, Zhang JJ, Wang ZZ, Cao LC (2018) Research on time-frequency analysis method of active earth pressure of rigid retaining wall subjected to earthquake. Environmental Earth Sciences 77(6):232, DOI: https://doi.org/10.1007/s12665-018-7325-6
Yao YP, Hou W, Zhou AN (2009) UH model: Three-dimensional unified hardening model for overconsolidated clays. Géotechnique 59(5):451–469, DOI: https://doi.org/10.1680/geot.2007.00029
Zhang LL, Fredlund DG, Fredlund MD, Wilson GW (2014) Modeling the unsaturated soil zone in slope stability analysis. Canadian Geotechnical Journal 51(12):1384–1398, DOI: https://doi.org/10.1139/cgj-2013-0394
Zhou AN, Huang RQ, Sheng DC (2016) Capillary water retention curve and shear strength of unsaturated soils. Canadian Geotechnical Journal 53(6):974–987, DOI: https://doi.org/10.1139/cgj-2015-0322
Zhou SW, Rabczuk T, Zhuang XY (2018a) Phase field modeling of quasi-static and dynamic crack propagation: COMSOL implementation and case studies. Advances in Engineering Software 122:31–49, DOI: https://doi.org/10.1016/j.advengsoft.2018.03.012
Zhou SW, Zhuang XY, Rabczuk T (2018b) A phase-field modeling approach of fracture propagation in poroelastic media. Engineering Geology 240:189–203, DOI: https://doi.org/10.1016/j.enggeo.2018.04.008
Zhou SW, Zhuang XY, Rabczuk T (2019a) Phase-field modeling of fluid-driven dynamic cracking in porous media. Computer Methods in Applied Mechanics and Engineering 350:169–198, DOI: https://doi.org/10.1016/j.cma.2019.03.001
Zhou SW, Zhuang XY, Rabczuk T (2019b) Phase field modeling of brittle compressive-shear fractures in rock-like materials: A new driving force and a hybrid formulation. Computer Methods in Applied Mechanics and Engineering 355:729–752, DOI: https://doi.org/10.1016/j.cma.2019.06.021
Zhou SW, Zhuang XY, Zhu HH, Rabczuk T (2018c) Phase field modelling of crack propagation, branching and coalescence in rocks. Theoretical and Applied Fracture Mechanics 96:174–192, DOI: https://doi.org/10.1016/j.tafmec.2018.04.011
Zhuang XY, Zhou SW, Sheng M, Li GS (2020) On the hydraulic fracturing in naturally-layered porous media using the phase field method. Engineering Geology 266:105306, DOI: https://doi.org/10.1016/j.enggeo.2019.105306
Acknowledgments
The research was financially support by the Systematic Project of Guangxi Key Laboratory of Disaster Prevention and Engineering Safety (Grant No. 2020ZDK010), the Fundamental Research Funds for the Central Universities (Grant No. JUSRP121055) and the National Key R&D Program of China (Grant No. 2018YFC1505105), and the National Natural Science Foundation of China (Grant Nos. 11672172 and 51709129). The authors appreciate the financial supports greatly.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, L., Xu, M., Li, J. et al. A New Method for Determination of 3D Active Earth Pressure of Unsaturated Backfills. KSCE J Civ Eng 25, 4631–4645 (2021). https://doi.org/10.1007/s12205-021-0508-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-021-0508-9