Abstract
Most studies of shallow foundations near slopes are commonly based on Mohr–Coulomb failure criterion, where the effect of intermediate principal stress on soil strength is not taken into account. However, true triaxial tests of soils have demonstrated that the intermediate principal stress notably enhances soil strength. In this study, a one-side failure mode with varying base roughness is adopted to derive the ultimate bearing capacity equation of strip foundations near slopes within the framework of the Meyerhof theory. The effect of intermediate principal stress on soil strength is governed by unified strength theory (UST). The flowchart of calculation steps for the proposed equation is provided with a trial method. The proposed equation is verified by comparing with model test results reported in the literature. Comparisons with a published theoretical solution show the ultimate bearing capacity of this study is larger due to allowing for the influence of soils in foundation depth. Parametric studies are investigated including the intermediate principal stress effect, the distance to slope crest, and the slope angle. It is found that the ultimate bearing capacity of a strip foundation near slopes is significantly increased with the intermediate principal stress effect, the distance to slope crest, and the base roughness, but it is markedly decreased with the slope angle. Moreover, the increasing rate decreases gradually with the distance to slope crest, and the ultimate bearing capacity finally converges to a stable value.
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Data availability
The data used to support the findings of this study are available from the corresponding author upon request.
References
Casablanca O, Biondi G, Cascone E, Filippo GD (2021) Static and seismic bearing capacity of shallow strip foundations on slopes. Géotechnique: 1–15. https://doi.org/10.1680/jgeot.20.P.044
Castelli F, Motta E (2010) Bearing capacity of strip footings near slopes. Geotech Geol Eng 28(2):187–198. https://doi.org/10.1007/s10706-009-9277-9
Chakraborty D, Kumar J (2003) Bearing capacity of foundations on slopes. Geomech Geoeng 8(4):274–285. https://doi.org/10.1080/17486025.2013.770172
Cinicioglu O, Erkli A (2018) Seismic bearing capacity of surficial foundations on sloping cohesive ground. Soil Dyn Earthquake Eng 111:53–64. https://doi.org/10.1016/j.soildyn.2018.04.027
Deng LS, Fan W, Yu MH (2018) Parametric study of a loess slope based on unified strength theory. Eng Geol 233:98–110. https://doi.org/10.1016/j.enggeo.2017.11.009
Gao JP, Yu MH, Li SP (2015) Double–shear unified solution of Terzaghi ultimate bearing capacity of foundation. Chin J Rock Mech Eng 24(15):2736–2740. https://doi.org/10.3321/j.issn:1000-6915.2005.15.023 (in Chinese)
Georgiadis K (2010) Undrained bearing capacity of strip footings on slopes. J Geotech Geoenviron Eng 136(5):677–685. https://doi.org/10.1061/ASCEGT.1943-5606.0000269
Halder K, Chakraborty D, Dash KS (2019) Bearing capacity of a strip footing situated on soil slope using a non–associated flow rule in lower bound limit analysis. Int J Geotech Eng 13(2):103–111. https://doi.org/10.1080/19386362.2017.1325119
Hansen JB (1970) A revised and extended formula for bearing capacity. Bull Dan Geotech Inst 28:5–11
Hu WD, Cao WG (2015) A simplified analysis method for the ultimate bearing capacity of ground foundation near slope based on the theory of Meyerhof. J Hunan Univ (Nat Sci) 42(1):81–89. https://doi.org/10.16339/j.cnki.hdxbzkb.2015.01.012 (in Chinese)
Huang CC (2019) Effects of restraining conditions on the bearing capacity of footings near slopes. Soils Found 59(1):1–12. https://doi.org/10.1016/j.sandf.2018.08.016
Izadi A, Kalourazi AF, Chenari RJ (2021) Effect of roughness on seismic bearing capacity of shallow foundations near slopes using the lower bound finite element method. Int J Geomech 21(3):06020043. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001935
Jahanandish M, Zeydabadinejad M (2019) An investigation on the effect of intermediate principal stress on the solution of bearing capacity problems by the method of stress characteristics. Geotech Geol Eng 37(5):4211–4227. https://doi.org/10.1007/s10706-019-00901-5
Jalili S, Koupaei HJ, Sharafi H, Ganjian N (2021) Experimental and numerical study of seismic behavior of shallow strip foundation near sandy slope. Int J Civ Eng: 1–18. https://doi.org/10.1007/s40999-021-00641-9
Jiao YY, Zhang Y, Tan F (2020) Estimation of active earth pressure against rigid retaining walls considering soil arching effects and intermediate principal stress. Int J Geomech 20(11):04020217. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001865
Kalourazi AF, Chenari RJ, Veiskarami M (2020) Bearing capacity of strip footings adjacent to anisotropic slopes using the lower bound finite element method. Int J Geomech 20(11):04020213. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001858
Keskin MS, Laman M (2013) Model studies of bearing capacity of strip footing on sand slope. KSCE J Civ Eng 17(4):699–711. https://doi.org/10.1007/s12205-013-0406-x
Keskin MS, Laman M (2014) Experimental and numerical studies of strip footings on geogrid–reinforced sand slope. Arab J Sci Eng 39(3):1607–1619. https://doi.org/10.1007/s13369-013-0795-7
Kusakabe O, Kimura T, Yamaguchi H (1981) Bearing capacity of slopes under strip loads on the top surfaces. Soils Found 21(4):29–40. https://doi.org/10.3208/sandf1972.21.4_29
Leshchinsky B (2015) Bearing capacity of footings placed adjacent to c′–ϕ′ slopes. J Geotech Geoenviron Eng 141(6):04015022. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001306
Li JC, Ma GW, Yu MH (2008) Penetration analysis for geo–material based on unified strength criterion. Int J Impact Eng 35(10):1154–1163. https://doi.org/10.1016/j.ijimpeng.2008.01.003
Li XF, Du SJ, Chen B (2017) Unified analytical solution for deep circular tunnel with consideration of seepage pressure, grouting and lining. J Cent South Univ 24(6):1483–1493. https://doi.org/10.1007/s1171-017-3552-3
Li Y, Zhao JH, Zhu Q, Cao XY (2015) Unified solution of burst pressure for defect–free thin walled elbows. J Press Vessel Technol 137(2):021203. https://doi.org/10.1115/1.4028068
Li ZX, Zhang CG, Zhao JY, Yan Q (2021) Safety factor of unsaturated soil slopes considering the intermediate principal stress effect and different profiles of matric suction. Math Probl Eng 2021:6622522. https://doi.org/10.1155/2021/6622522
Luo N, Bathurst RJ (2017) Reliability bearing capacity analysis of footings on cohesive soil slopes using RFEM. Comput Geotech 89:203–212. https://doi.org/10.1016/j.compgeo.2017.04.013
Ma ZY, Liao HJ, Dang FN (2014) Influence of intermediate principal stress on the bearing capacity of strip and circular footings. J Eng Mech 140(7):04014041. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000762
Mahabadi O, Kaifosh P, Marschall P, Vietor T (2014) Three–dimensional FDEM numerical simulation of failure processes observed in Opalinus Clay laboratory samples. J Rock Mech Geotech Eng 6(6):591–606. https://doi.org/10.1016/j.jrmge.2014.10.005
Meryerhof GG (1957) The ultimate bearing capacity of foundations on slopes. In: Proceedings of the 4th International Conference on Soil Mechanics and Foundation Engineering. London, UK, p 384–386. https://doi.org/10.1080/17486025.2013.770172
Meyerhof GG (1963) Some recent research on the bearing capacity of foundations. Can Geotech J 1(1):16–26. https://doi.org/10.1139/t63-003
Nakai T, Matsuoka H (1983) Shear behaviors of sand and clay under three–dimensional stress condition. Soils Found 23(2):26–42. https://doi.org/10.3208/sandf1972.23.2_26
Narita K, Yamaguchi H (1990) Bearing capacity analysis of foundations on slopes by use of log–spiral sliding surfaces. Soils Found 30(3):144–152. https://doi.org/10.3208/sandf1972.30.3_144
Prashant A, Penumadu D (2004) Effect of intermediate principal stress on overconsolidated kaolin clay. J Geotech Geoenviron Eng 130(3):284–292. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:3(284)
Rouchi JM, Farzaneh O, Askari F (2014) Bearing capacity of strip footings near slopes using lower bound limit analysis. Civ Eng Infrastruct J 47(1):89–109. https://doi.org/10.7508/ceij.2014.01.007
Terzaghi K (1943) Theoretical soil mechanics. John Wiley & Sons, New York
Vesic AS (1973) Analysis of ultimate loads of shallow foundations. J Soil Mech and Found Div 99(1):45–73. https://doi.org/10.1016/0148-9062(74)90598-1
Wang G, Liu Z, Wang P, Guo Y, Li W (2019) The effect of gas migration on the deformation and permeability of coal under the condition of true triaxial stress. Arab J Geosci 12(15):486. https://doi.org/10.1007/s12517-019-4630-7
Wang HY, Yang M (2005) An estimate for the loss of bearing capacity of the footing near excavations. China Civ Eng J 38(8):95–101. https://doi.org/10.1007/s11769-005-0030-x (in Chinese)
Wu GQ, Zhang R, Zhao MH, Zhou S (2020a) Undrained stability analysis of eccentrically loaded strip footing lying on layered slope by finite element limit analysis. Comput Geotech 123:103600. https://doi.org/10.1016/j.compgeo.2020.103600
Wu GQ, Zhao H, Zhao MH, Xiao Y (2020b) Undrained seismic bearing capacity of strip footings lying on two–layered slopes. Comput Geotech 122:103539. https://doi.org/10.1016/j.compgeo.2020.103539
Wu GQ, Zhao MH, Zhang R, Lei M (2021a) Ultimate bearing capacity of strip footings on Hoek-Brown rock slopes using adaptive finite element limit analysis. Rock Mech Rock Eng 54(3):1621–1628. https://doi.org/10.1007/s00603-020-02334-6
Wu GQ, Zhao MH, Zhao H (2021b) Undrained seismic bearing capacity of strip footings horizontally embedded in two–layered slopes. Earthq Spectra 37(2):637–651. https://doi.org/10.1177/8755293020957332
Yang XL, Wang ZB, Zou JF, Li L (2007) Bearing capacity of foundation on slope determined by energy dissipation method and model experiments. J Cent South Univ Technol 14(1):125–128. https://doi.org/10.1007/s11771-007-0025-0
Yoshimine M, Ishihara K, Vargas W (1998) Effects of principal stress direction and intermediate principal stress on undrained shear behavior of sand. Soils Found 38(3):179–188. https://doi.org/10.3208/sandf.38.3_179
Yu MH (1998) Twin–shear theory and its application. Science Press, Beijing (in Chinese)
Yu MH (2004) Unified strength theory and its applications. Springer & Verlag, Berlin, Heidelberg
Yu MH, Wu XX, Jun Shi, Zhou GC (2020) A new method for determining soil failure criteria. J Xi’an Jiaotong Univ 54(8):1–10. https://doi.org/10.7652/xjtuxb202008001 (in Chinese)
Zhang CG, Cai MM, Qi H, Shan YP (2019) A unified solution for calculating mine backfills considering the backfilling order and the back wall cohesion. Chin J Rock Mech Eng 38(2):15–25. https://doi.org/10.13722/j.cnki.jrme.2018.0899 (in Chinese)
Zhang CG, Wang JF, Zhao JH (2010) Unified solutions for stresses and displacements around circular tunnels using the unified strength theory. Sci China Tech Sci 53(6):1694–1699. https://doi.org/10.1007/s11431-010-3224-0
Zhang CG, Yan Q, Zhao JH, Wang JT (2020) Formulation of ultimate bearing capacity for strip foundations based on the Meyerhof theory and unsaturated soil mechanics. Comput Geotech 126:103734. https://doi.org/10.1016/j.compgeo.2020.103734
Zhao JH, Zhai Y, Ji L, Wei XY (2007) Unified solutions to the limit load of thick–walled vessels. J Press Vessel Technol 129(4):670–675. https://doi.org/10.1115/1.2767356
Zhou HZ, Zheng G, Yin X, Jia R, Yang XY (2018) The bearing capacity and failure mechanism of a vertically loaded strip footing placed on the top of slopes. Comput Geotech 94:12–21. https://doi.org/10.1016/j.compgeo.2017.08.009
Zhou XP, Yang HQ, Zhang YX, Yu MH (2009) The effect of the intermediate principal stress on the ultimate bearing capacity of a foundation on rock masses. Comput Geotech 36(5):861–870. https://doi.org/10.1016/j.compgeo.2009.01.009
Zou JF, Xia ZQ (2017) Closed–form solution for cavity expansion in strain–softening and undrained soil mass based on the unified strength failure criterion. Int J Geomech 17(9):04017046. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000927
Funding
The financial supports are provided by the National Natural Science Foundation of China (NSFC) (Nos. 51878056 and 41202191), the Opening Fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (No. SKLGP2020K022), the Social Development Foundation for Science and Technology Planning Project of Shaanxi Province (No. 2019SF–256), and the Fundamental Research Funds for the Central Universities, CHD (Nos. 300102289720 and 300102280108).
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Responsible Editor: Zeynal Abiddin Erguler
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Yan, Q., Zhao, J. & Zhang, C. Ultimate bearing capacity of a strip foundation near slopes based on the unified strength theory. Arab J Geosci 14, 2218 (2021). https://doi.org/10.1007/s12517-021-08619-6
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DOI: https://doi.org/10.1007/s12517-021-08619-6