Abstract
In extant studies, most of the analyses on active earth pressure focused on dry or saturated soils using two-dimensional failure mechanisms. However, in practice, soils are usually unsaturated, and all failures of retained soil masses indicate a somewhat three-dimensional (3D) feature. This work adopts the kinematic limit analysis method to evaluate the active earth pressure with considering the 3D effect and the presence of vertical steady unsaturated seepage. A closed-form framework for describing the profile of suction stress is adopted, and an extended form of the Mohr–Coulomb failure criterion is introduced to represent the unsaturated soil strength. In the context of a 3D horn-like collapse mechanism, the resultant of active earth pressure is evaluated and expressed as a dimensionless coefficient. Several charts are provided for parametric studies. The obtained results indicate that accounting for either the presence of unsaturated seepage or the 3D effect can lead to a more economical result. This study considers a more realistic service behavior of retaining structures and presents a useful solution for the 3D active earth pressure under unsaturated seepage conditions.
References
Antão AN, Santana TG, da Silva MV, Guerra NM (2016) Three-dimensional active earth pressure coefficients by upper bound numerical limit analysis. Comput Geotech 79:96–104
Bishop AW (1959) The principle of effective stress. Tek Ukeblad 106(39):859–863
Chen WF (1975) Limit analysis and soil plasticity. Elsevier, Amsterdam
Escario V, Saez J (1986) The shear strength of partly saturated soils. Géotechnique 36(3):453–456
Fredlund DG, Morgenstern NR, Widger RA (1978) The shear strength of unsaturated soils. Can Geotech J 15(3):313–321
Gardner WR (1958) Steady state solutions of the unsaturated moisture flow equation with application to evaporation from a water table. Soil Sci 85:228–232
Griffiths DV, Lu N (2005) Unsaturated slope stability analysis with steady infiltration or evaporation using elasto-plastic finite elements. Int J Numer Anal Meth Geomech 29(3):249–267
Huder J (1972) Stability of bentonite slurry trenches with some experiences in Swiss practice. Proc 5th Eur Conf Soil Mech Found Eng 4(9):517–522
Khalili N, Geiser F, Blight GE (2004) Effective stress in unsaturated soils: Review with new evidence. Int J Geomech 4(2):115–126
Khalili N, Khabbaz MH (1998) A unique relationship of χ for the determination of the shear strength of unsaturated soils. Geotechnique 48(5):681–687
Li TZ, Yang XL (2019) 3D rotational failure mechanism of tunnel face in weathered and saturated Hoek-Brown rock masses. KSCE J Civ Eng 23(6):2723–2732
Li YX, Yang XL (2019) Seismic displacement of 3D slope reinforced by piles with nonlinear failure criterion. Int J Geomech 19(6):04019042
Li ZW, Yang XL (2019) Active earth pressure for retaining structures in cohesive backfills with tensile strength cut-off. Comput Geotech 110:242–250
Li ZW, Yang XL (2019) Active earth pressure from unsaturated soils with different water levels. Int J Geomech 19(7):06019013
Liang WB, Zhao JH, Li Y, Zhang CG, Wang S (2012) Unified solution of Coulomb’s active earth pressure for unsaturated soils without crack. Appl Mech Mater 170:755–761
Lu N, Godt JW, Wu DT (2010) A closed-form equation for effective stress in unsaturated soil. Water Resour Res 46(5):W05515
Lu N, Likos WJ (2006) Suction stress characteristic curve for unsaturated soil. J Geotech Geoenviron Eng 132(2):131–142
Lu N, Likos WJ (2004) Unsaturated soil mechanics. Wiley, New York
Michalowski RL, Drescher A (2009) Three-dimensional stability of slopes and excavations. Géotechnique 59(10):839–850
Nuth M, Laloui L (2008) Effective stress concept in unsaturated soils: Clarification and validation of a unified framework. Int J Numer Anal Meth Geomech 32(7):771–801
Pan Q, Dias D (2017) Probabilistic evaluation of tunnel face stability in spatially random soils using sparse polynomial chaos expansion with global sensitivity analysis. Acta Geotech 12(6):1415–1429
Pan Q, Dias D (2018) Three-dimensional static and seismic stability analysis of a tunnel face driven in weak rock masses. Int J Geomech 18(6):04018055
Pan Q, Xu J, Dias D (2017) Three-dimensional stability of a slope subjected to seepage forces. Int J Geomech 17(8):04017035
Pufahl DE, Fredlund DG, Rahardjo H (1983) Lateral earth pressures in expansive clay soils. Can Geotech J 20(2):228–241
Soubra AH, Macuh B (2002) Active and passive earth pressure coefficients by a kinematical approach. Proc ICE Geotech Eng 155(2):119–131
Sun YJ, Song EX (2016) Active earth pressure analysis based on normal stress distribution function along failure surface in soil obeying nonlinear failure criterion. Acta Geotech 11(2):255–268
Tom Wörden F, Achmus M (2013) Numerical modeling of three-dimensional active earth pressure acting on rigid walls. Comput Geotech 51:83–90
Vahedifard F, Leshchinsky BA, Mortezaei K, Lu N (2015) Active earth pressures for unsaturated retaining structures. J Geotech Geoenviron Eng 141(11):04015048
Vahedifard F, Leshchinsky D, Mortezaei K, Lu N (2016) Effective stress-based limit-equilibrium analysis for homogeneous unsaturated slopes. Int J Geomech 16(6):D4016003
Vanapalli SK, Fredlund DG, Pufahl DE, Clifton AW (1996) Model for the prediction of shear strength with respect to soil suction. Can Geotech J 33(3):379–392
Xu SY, Lawal AI, Shamsabadi A, Taciroglu E (2019) Estimation of static earth pressures for a sloping cohesive backfill using extended Rankine theory with a composite log-spiral failure surface. Acta Geotech 14(2):579–594
Yang XL, Li ZW (2018) Upper bound analysis of 3D static and seismic active earth pressure. Soil Dyn Earthq Eng 108:18–28
Zhai Q, Rahardjo H (2012) Determination of soil–water characteristic curve variables. Comput Geotech 42:37–43
Zhai Q, Rahardjo H (2015) Estimation of permeability function from the soil-water characteristic curve. Eng Geol 199:148–156
Zhai Q, Rahardjo H, Satyanaga A (2017) Effects of residual suction and residual water content on the estimation of permeability function. Geoderma 303:165–177
Zhang DB, Jiang Y, Yang XL (2019) Estimation of 3D active earth pressure under nonlinear strength condition. Geomech Eng 17(6):515–525
Zhang LL, Fredlund DG, Fredlund MD, Wilson GW (2014) Modeling the unsaturated soil zone in slope stability analysis. Can Geotech J 51(12):1384–1398
Zhang R, Yang XL (2019) Limit analysis of anchor trapdoor embedded in nonhomogeneous and nonlinear soils. Int J Geomech 19(8):04019089
Zou J, Chen K, Pan Q (2018) An improved numerical approach in surrounding rock incorporating rockbolt effectiveness and seepage force. Acta Geotech 13(3):707–727
Acknowledgements
The present work was funded by National Basic Research 973 Program of China (2013CB036004). The financial support is greatly appreciated.
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Li, Z., Yang, X. Three-dimensional active earth pressure for retaining structures in soils subjected to steady unsaturated seepage effects. Acta Geotech. 15, 2017–2029 (2020). https://doi.org/10.1007/s11440-019-00870-2
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DOI: https://doi.org/10.1007/s11440-019-00870-2