Abstract
Rigid piles have been widely used to reinforce soft subgrade. However, some studies do not consider the bending failure of piles and wedge sliding surfaces, which may lead to an overestimation of stability. In this study, a stability calculation method for a multi-section linear sliding surface is first derived and then simplified to three-part wedge method based on the numerical modeling of the failure evolution process. The real safety factor is replaced by the average value of the upper and lower bound solutions of the embankment stability safety factor. Through calculations, then the average value or the approximate solution of the real value, of both the upper and lower bound solutions can be obtained. The accuracy of the approximate solution can be verified through an analysis of the relative error of the average and true values. Finally, the proposed method was verified by a three-dimensional numerical simulation method and compared with the traditional limit equilibrium method and the equivalent shear strength parameter method. The results indicate that the support contribution of rigid piles to the embankment can be effectively reflected by considering wedge sliding surfaces, and a more reasonable stability safety factor can be obtained through the proposed method.
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Abbreviations
- B :
-
Width of the crest of the embankment (m)
- c :
-
Cohesive force of the soil in the wedge sliding surface (kPa)
- c′:
-
Cohesive force of the soil at the wedge sliding surface (kPa)
- C h :
-
Cohesive force of the soil in the wedge element at the sliding surface (kN/m)
- C v :
-
Cohesive force between the wedge element and adjacent wedges (kN/m)
- e :
-
Absolute error of the approximate solution compared with the real stability safety factor of the embankment
- e max :
-
Upper limit of the absolute error
- E i, E i+1(i=1,2,3…) :
-
Normal forces exerted by adjacent wedges (kN/m)
- E 0 :
-
Modulus of elasticity (MPa)
- F i(i=1,2,3…) :
-
Tangential force of the bottom of the slip surface acting on the wedge element (kN/m)
- H 1 :
-
Height of the Wedge 1 (m)
- H 2 :
-
Height of the Wedge 3 (m)
- J :
-
Multiple of the soil deformation modulus
- K :
-
Overall stability and safety coefficient of the embankment
- K ave :
-
Average value of Kmax and Kmin
- K max :
-
Upper bound solution of the embankment stability safety factor
- K min :
-
Lower bound solution of the embankment stability safety factor
- K true :
-
Real safety factor
- K v :
-
Safety coefficients of the interfaces between the wedges
- L :
-
Pile length above the wedge sliding surface (m)
- m :
-
Number of piles in the wedge element
- M :
-
Bending strength of the pile (kN·m/m)
- M 1 :
-
Anti-sliding moment contributed by the bending strength of the pile (kN·m/m)
- M 2 :
-
Anti-sliding moment contributed by the equivalent resistance of the pile at the sliding surface (kN·m/m)
- n :
-
Number of polyline segments of the sliding surface
- N i(i=1,2,3…) :
-
Normal force of the bottom of the slip surface acting on the wedge element (kN/m)
- P :
-
Anti-sliding concentrated force of the pile (kN/m)
- Q i(i=1,2,3…) :
-
Equivalent resistance of the pile in the wedge element at the sliding surface (kN/m)
- Q t :
-
Equivalent resistance of the t-th pile in the wedge element at the wedge sliding surface (kN/m)
- R :
-
Radius of the inscribed circle of the wedge sliding surface (m)
- T :
-
Ratio between the maximum shear force and the maximum bending moment of the pile in the whole model (m−1)
- W i(i = 1,2,3…) :
-
Weight of the wedge element (kN/m)
- X i, X i+1(i=1,2,3…):
-
Tangential forces exerted by adjacent wedges (kN/m)
- α :
-
Angle between the sliding surface and horizontal direction of Wedge 1 in the three-part wedge model (°)
- β :
-
Angle between the sliding surface and horizontal direction of Wedge 2 in the three-part wedge model (°)
- γ :
-
Unit weight of the soil in the wedge sliding surface (kN/m3)
- δ :
-
Internal friction angle of the soil at the wedge sliding surface (°)
- ε :
-
Relative error of the approximate solution compared with the real stability safety factor of the embankment
- εmax :
-
Upper limit of the relative error
- θi(i=1,2,3…) :
-
Angle between the slip line and the horizontal direction (°)
- μ :
-
Poisson’s ratio
- φ :
-
Internal friction angle of the soil in the wedge sliding surface (°)
References
ABACUS (1996) User’s manual. Dassault Systèmes Simulia Corp., Province, RI, USA
Abusharar SW, Han J (2011) Two-dimensional deep-seated slope stability analysis of embankments over stone column-improved soft clay. Engineering Geology 120(1–4):103–110, DOI: https://doi.org/10.1016/j.enggeo.2011.04.002
Chen ZY (2003) Soil slope stability analysis: Theory, methods and programs. China Water Power Press, Beijing, China (in Chinese)
Cooper MR, Rose AN (1999) Stone column support for an embankment on deep alluvial soils. Proceedings of the Institution of Civil Engineers-Geotechnical Engineering 137(1):15–25, DOI: https://doi.org/10.1680/gt.1999.370103
Deb K, Dhar A, Bhagat P (2012) Evolutionary approach for optimal stability analysis of geosynthetic-reinforced stone column-supported embankments on clay. KSCE Journal of Civil Engineering 16(11): 1185–1192, DOI: https://doi.org/10.1007/s12205-012-1797-9
Han J (2014) Principles and practice of ground improvement. John Wiley & Sons, Inc., Hoboken, NJ, USA
Han J, Chai JC, Leshchinsky D, Shen SL (2004) Evaluation of deep-seated slope stability of embankments over deep mixed foundations. American Society of Civil Engineers GeoSupport Conference 163–171, DOI: https://doi.org/10.1061/40713(2004)71
Han J, Huang J, Porbaha A (2005) 2D numerical modeling of a constructed geosynthetic-reinforced embankment over deep mixed columns. Geo-frontiers Congress, DOI: https://doi.org/10.1061/40777(156)13
Hashizume H (1998) Study on the behavior of soft ground improved using deep mixing method. Proceeding of the international conference on centrifuge, September 23–25, Tokyo, Japan, 851–856
Kitazume M, Maruyama K (2005) Collapse failure of group column type deep mixing improved ground under embankment. Proceeding of the international conference on centrifuge, January 8–9, Tokyo, Japan, 245–254
Kitazume M, Okano K, Miyajima S (2001) Centrifuge model tests on failure envelope of column type deep mixing method improved ground-closure. Soils and Foundations 41(4):108–108, DOI: https://doi.org/10.3208/sandf.40.4_43
Miyake M, Akamoto H, Wada M (1991) Deformation characteristics of ground improved by a group of treated soil. Proceeding of the international conference on centrifuge, June 13–14, Boulder, CO, USA, 295–302
Navin MP, Filz GM (2006) Numerical stability analyses of embankments supported on deep mixed columns. Geoshanghai international conference, June 6–8, Shanghai, China, DOI: https://doi.org/10.1061/40864(196)1
Qian X, Koerner RM (2004) Effect of apparent cohesion on translational failure analyses of landfills. Journal of Geotechnical and Geoenvironmental Engineering 130(1):71–80, DOI: https://doi.org/10.1061/(asce)1090-0241(2004)130:1(71)
Qian X, Koerner RM, Gray DH (2003) Translational failure analysis of landfills. Journal of Geotechnical and Geoenvironmental Engineering 129(6):506–519, DOI: https://doi.org/10.1061/(asce)1090-0241(2003)129:6(506)
Su Q (2013) Deformation and failure modes of composite foundation with sub-embankment plain concrete piles. Sciences in Cold and Arid Regions 5(5):614–625
Tan SA, Tjahyono S, Oo KK (2008) Simplified plane-strain modeling of stone-column reinforced ground. Journal of Geotechnical and Geoenvironmental Engineering 134(2):185–194, DOI: https://doi.org/10.1061/(asce)1090-0241(2008)134:2(185)
Tassios TP, Vintzeleou EN (1988) Concrete-to-concrete friction-closure. Journal of Structural Engineering 114(12):2827–2828, DOI: https://doi.org/10.1061/(ASCE)0733-9445(1988)114:12(2827)
Wu CQ, Xiao DP (2007) Stability analysis of embankment on composite subgrade. Rock and Soil Mechanics 28:905–908 (in Chinese)
Yapage NNS, Liyanapathirana DS, Kelly RB, Poulos HG, Leo CJ (2014) Numerical modeling of an embankment over soft ground improved with deep cement mixed columns: Case history. Journal of Geotechnical and Geoenvironmental Engineering 140(11), DOI: https://doi.org/10.1061/(asce)gt.1943-5606.0001165
Yapage NNS, Liyanapathirana DS, Leo CJ (2013) Failure modes for geosynthetic reinforced column supported (grcs) embankments. Proceedings of the 18th international conference on soil mechanics and geotechnical engineering, September 2–6, Paris, France, 849–852
Yapage NNS, Liyanapathirana DS, Poulos HG, Kelly RB, Leo CJ (2012) An investigation of progressive failure of geosynthetic reinforced deep cement mixed column supported embankments. International conference on ground improvement and ground control, October 30–November 2, Wollong, Australia, 1345–1351
Yapage NNS, Liyanapathirana DS, Poulos HG, Kelly RB, Leo CJ (2015) Numerical modeling of geotextile-reinforced embankments over deep cement mixed columns incorporating strain-softening behavior of columns. International Journal of Geomechanics 15(2), DOI: https://doi.org/10.1061/(asce)gm.1943-5622.0000341
Yu JL, Zhong JN, Li JY, Xu RQ, Gong XN (2018) Centrifugal model tests on working behavior of composite foundation reinforced by rigid piles with caps under embankment. Proceedings of China-Europe conference on geotechnical engineering, August 13–16, Vienna, Austria, 1077–1080
Zheng G, Liu L, Han J (2010) Stability of embankment on soft subgrade reinforced by rigid inclusions(ii)group piles analysis. Chinese Journal of Geotechnical Engineering 32(12):1811–1820 (in Chinese)
Zheng G, Yang XY, Zhou HZ, Chai JC (2019) Numerical modeling of progressive failure of rigid piles under embankment load. Canadian Geotechnical Journal 56(1):23–34, DOI: https://doi.org/10.1139/cgj-2017-0613
Zheng G, Yu D, Shuai L, Jie H (2013) Stability failure modes of rigid column-supported embankments. Geo-congress 2013, March 3–7, San Diego, CA, USA, DOI: https://doi.org/10.1061/9780784412787.181
Acknowledgements
This study is financially supported by the National Natural Science Foundation of China (No. 41572253).
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Liu, P., Xiong, Cx. & Chen, Fq. Three-Part Wedge Method for the Stability Calculation of Embankment Supported on Rigid Pile Foundation. KSCE J Civ Eng 24, 794–806 (2020). https://doi.org/10.1007/s12205-020-1513-0
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DOI: https://doi.org/10.1007/s12205-020-1513-0