Abstract
Ensuring a safe foundation design in soft clay is always a challenging task to engineers. In the present study, the effectiveness of under-reamed piles in soft clay underlaid by stiff clay is numerically studied using the lower-bound finite element limit analysis (LB FELA). The bearing and uplift capacities of under-reamed piles are estimated through non-dimensional factors Ncul and Fcul, respectively. These factors increased remarkably and marginally compared to Ncul and Fcul of the piles without bulbs when the bulb is placed in stiff and soft clay, respectively. For a given ratio of undrained cohesion of stiff to soft clay (c2/c1), the factors Ncul and Fcul moderately increased with the increase in the length-to-shaft-diameter ratio (Lu/D) and adhesion factors in soft clay (αs1) and stiff clay (αs2). The variation of radial stress along the pile-soil interface, distribution of axial force in the under-reamed piles, and state of plastic shear failure in the soil are also studied under axial compression and tension. The results of this study are expected to be useful for the estimation of the bearing and uplift capacities of under-reamed piles in uniform clay and soft clay underlaid by stiff clay.
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Abbreviations
- a :
-
a component of the equation representing the Mohr-Coulomb yield criteria
- A s :
-
area of the cross-section of the shaft
- c :
-
undrained cohesion of soil
- c 1 :
-
undrained cohesion of soft clay
- c 2 :
-
undrained cohesion of stiff clay
- d :
-
a component of the equation representing the Mohr-Coulomb yield criteria
- dr i, dz i :
-
radial and vertical distances between the lower and upper nodes of the ith edge along the shaft and surfaceof bulbs, respectively
- D :
-
shaft diameter
- D u :
-
bulb diameter
- e base :
-
number of edges at the pile base
- e s,1, e s,2 :
-
total edges along the shaft below and above the bulb, respectively
- e bs,1 e ts,1 :
-
total edges along the bottom and top surfaces of the bulb, respectively
- F cul :
-
non-dimensional uplift capacity factor for the layered clay
- h b :
-
distance of the centre of the bulb from the pile base
- LB FELA :
-
lower-bound finite element limit analysis
- L 1 :
-
depth of the soft clay (top) layer
- L 2 :
-
depth of the stiff clay (bottom) layer
- L h :
-
horizontal domain extent from the pile surface
- L u :
-
depth of embedment of the under-reamed pile from the ground level
- L v :
-
vertical domain extent below the pile base
- N cul :
-
non-dimensional bearing capacity factor for the layered clay
- Q cl :
-
ultimate collapse load under axial compression for the layered clay
- Q cl,base :
-
resistance from the base under axial compression
- Q cl,bulb :
-
resistance from the bulb under axial compression
- Q cl,shaft :
-
resistance from the shaft under axial compression
- Q ul :
-
ultimate collapse load under axial tension for the layered clay
- Q ul,base :
-
resistance from the base under axial tension
- Q ul,bulb :
-
resistance from the bulb under axial tension
- Q ul,shaft :
-
resistance from the shaft under axial tension
- r i, r i+1 :
-
radial distance of the ith and (i + 1)th nodes along the pile base from the pile center
- r 1,i, r u,i :
-
radial distance of the lower and upper nodes of the ith edge along the bottom and top surfaces of the bulb
- α b :
-
adhesion factor at the pile base
- α s :
-
pile-soil adhesion factor along shaft
- α s1, α s2 :
-
pile-soil adhesion factor of soft and stiff clay, respectively
- β :
-
angle of the bulb surface with respect to the horizontal plane (under-ream angle)
- γ :
-
unit weight of soil
- σ r :
-
normal stress in the r-direction
- σ z :
-
normal stress in the z-direction
- τ nt :
-
tangential stress along the surface of the bulb
- τ rz :
-
shear stress in the r-z plane
References
Meyerhof G G. Some recent research on the bearing capacity of foundations. Canadian Geotechnical Journal, 1963, 1(1): 16–26
Coyle H M, Reese L C. Load transfer for axially loaded piles in clay. Journal of the Soil Mechanics and Foundations Division, 1966, 92(2): 1–26
Vesic A S. A Study of Bearing Capacity of Deep Foundations. Final Report, Project B-189. Atlanta: Georgia Institute of Technology, 1967
Poulos H G. The influence of shaft length on pile load capacity in clays. Geotechnique, 1982, 32(2): 145–148
Zhou H, Chen Z. Analysis of effect of different construction methods of piles on the end effect on skin friction of piles. Frontiers of Architecture and Civil Engineering in China, 2007, 1(4): 458–463
Khatri V N, Kumar J. Bearing capacity factor Nc under ϕ = 0 condition for piles in clays. International Journal for Numerical and Analytical Methods in Geomechanics, 2009, 33(9): 1203–1225
Chakraborty D, Kumar J. Bearing capacity of piles in soft clay underlaid by cohesive frictional soil. International Journal of Geomechanics, 2013, 13(3): 311–317
Ismail A. ANN-based empirical modelling of pile behaviour under static compressive loading. Frontiers of Structural and Civil Engineering, 2018, 12(4): 594–608
Meyerhof G G, Adams J I. The ultimate uplift capacity of foundations. Canadian Geotechnical Journal, 1968, 5(4): 225–244
Das B M. A procedure for estimation of ultimate uplift capacity of foundations in clay. Soil and Foundation, 1980, 20(1): 77–82
Das B M, Seeley G R. Uplift capacity of pipe piles in saturated clay. Soil and Foundation, 1982, 22(1): 91–94
Shin E C, Das B M, Puri V K, Yen S C, Cook E E. Ultimate uplift capacity of model rigid metal piles in clay. Geotechnical and Geological Engineering, 1993, 11(3): 203–215
Veeresh C, Rao S N. Vertical pullout capacity of model batter anchor piles in marine clays. Marine Georesources and Geotechnology, 1996, 14(3): 205–215
Khatri V N, Kumar J. Uplift capacity of axially loaded piles in clays. International Journal of Geomechanics, 2011, 11(1): 23–28
Cooke R W, Whitaker T. Experiments on model piles with enlarged bases. Geotechnique, 1961, 11(1): 1–13
Mohan D, Murthy V N S, Jain G S. Design and construction of multi-under-reamed piles. In: Proceedings of the 7th International Conference on Soil Mechanics and Foundation Engineering. Mexico, 1969, 183–186
Martin R E, DeStephen R. Large diameter double under-reamed drilled shafts. Journal of Geotechnical Engineering, 1983, 109(8): 1082–1098
Prakash S, Sharma H D. Pile Foundations in Engineering Practice. New York: Wiley-Interscience, 1990
Peter J A, Lakshmanan N, Devadas Manoharan P. Investigations on the static behavior of self-compacting concrete under-reamed piles. Journal of Materials in Civil Engineering, 2006, 18(3): 408–414
Shrivastava N, Bhatia N. Ultimate bearing capacity of under-reamed pile-finite element approach. In: The 12th International Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG). Goa, India, 2008, 1–6
Kurian N P, Srilakshmi G. Studies on the geometrical features of under-reamed piles by the finite element method. Journal of Karunya University, 2010, 2(1): 1–14
Watanabe K, Sei H, Nishiyama T, Ishii Y. Static axial reciprocal load test of cast-in-place nodular concrete pile and nodular diaphragm wall. Geotechnical Engineering Journal of the SEAGS & AGSSEA, 2011, 42(2): 11–19
Kong G Q, Yang Q, Liu H L, Liang R Y. Numerical study of a new belled wedge pile type under different loading modes. European Journal of Environmental and Civil Engineering, 2013, 17(sup1): s65–82
Farokhi A S, Alielahi H, Mardani Z. Optimizing the performance of under-reamed piles in clay using numerical method. Electronic Journal of Geotechnical Engineering, 2014, 19: 1507–1520
Vali R, Mehrinejad Khotbehsara E, Saberian M, Li J, Mehrinejad M, Jahandari S. A three-dimensional numerical comparison of bearing capacity and settlement of tapered and under-reamed piles. International Journal of Geotechnical Engineering, 2019, 13(3): 236–248
Kumar A, Khatri V N, Gupta S K. Effect of linearly increasing cohesion on the compression and uplift capacity of the under-reamed pile in clay. SN Applied Sciences, 2020, 2(2): 315
Golait Y S, Padade A H, Cherian T. Prediction of quantitative response of under-reamed anchor piles in soft clay using laboratory model study. Journal of Testing and Evaluation, 2017, 46(2): 507–522
Khatri V N, Kumar A, Gupta S K, Dutta R K, Gnananandarao T. Numerical study on the uplift capacity of under-reamed piles in clay with linearly increasing cohesion. International Journal of Geotechnical Engineering, 2019 (in press)
Zienkiewicz O C, Taylor R L, Nithiarasu P, Zhu J Z. The Finite Element Method. London: McGraw-Hill, 1977
Hughes T J R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Mineola, NY: Dover Publications, 2000
Rabczuk T, Belytschko T. Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343
Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455
Nguyen V P, Anitescu C, Bordas S P, Rabczuk T. Isogeometric analysis: An overview and computer implementation aspects. Mathematics and Computers in Simulation, 2015, 117: 89–116
Hughes T J, Sangalli G, Tani M. Isogeometric Analysis: Mathematical and Implementational Aspects, with Applications. Insplines and PDEs: From Approximation Theory to Numerical Linear Algebra. Cham: Springer, 2018, 237–315
Anitescu C, Atroshchenko E, Alajlan N, Rabczuk T. Artificial neural network methods for the solution of second order boundary value problems. Computers, Materials & Continua, 2019, 59(1): 345–359
Samaniego E, Anitescu C, Goswami S, Nguyen-Thanh V M, Guo H, Hamdia K, Zhuang X, Rabczuk T. An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications. Computer Methods in Applied Mechanics and Engineering, 2020, 362: 112790
Rabczuk T, Ren H, Zhuang X. A nonlocal operator method for partial differential equations with application to electromagnetic waveguide problem. Computers. Materials and Continua, 2019, 59(1): 31–55
IS 2911 Part III. Indian Standard Code of Practice for Design and Construction of Pile Foundations (Part-III): Under-Reamed Piles. 1st ed. New Delhi: Bureau of Indian Standards, 1980
Chen W F, Liu X L. Limit Analysis in Soil Mechanics. Amsterdam: Elsevier Science, 1990
Makrodimopoulos A, Martin C M. Lower bound limit analysis of cohesive-frictional materials using second-order cone programming. International Journal for Numerical Methods in Engineering, 2006, 66(4): 604–634
Keawsawasvong S, Ukritchon B. Undrained stability of an active planar trapdoor in non-homogeneous clays with a linear increase of strength with depth. Computers and Geotechnics, 2017, 81: 284–293
Bottero A, Negre R, Pastor J, Turgeman S. Finite element method and limit analysis theory for soil mechanics problems. Computer Methods in Applied Mechanics and Engineering, 1980, 22(1): 131–149
Sloan S W. Lower bound limit analysis using finite elements and linear programming. International Journal for Numerical and Analytical Methods in Geomechanics, 1988, 12(1): 61–77
Griffiths D V. Elasto-plastic analyses of deep foundations in cohesive soil. International Journal for Numerical and Analytical Methods in Geomechanics, 1982, 6(2): 211–218
NAVFAC DM (Naval Facilities Engineering Command Design Manual) 7.2. Foundation and Earth Structures. Alexandria: U.S. Department of the Navy, 1984
Tomlinson M J. Pile Design and Construction Practice. 4th ed. London: E and F N Spon, 1994
Salgado R, Lyamin A V, Sloan S W, Yu H S. Two-and three-dimensional bearing capacity of foundations in clay. Geotechnique, 2004, 54(5): 297–306
Martin C M, Randolph M F. Applications of the lower and upper bound theorems of plasticity to collapse of circular foundations. In: Proceedings of the 10th International Conference on Computer Methods and Advances in Geomechanics. Abingdon: Taylor and Francis, 2001, 2: 1417–1428
Nguyen V Q. Numerical modelling of the undrained vertical bearing capacity of shallow foundations. Thesis for the Master’s Degree. Queensland: University of Southern Queensland, 2008
Clark J I, Meyerhof G G. The behavior of piles driven in clay. An investigation of soil stress and pore water pressure as related to soil properties. Canadian Geotechnical Journal, 1972, 9(4): 351–373
Randolph M F, Carter J P, Wroth C P. Driven piles in clay-the effects of installation and subsequent consolidation. Geotechnique, 1979, 29(4): 361–393
Zhou S, Zhuang X, Rabczuk T. A phase-field modeling approach of fracture propagation in poroelastic media. Engineering Geology, 2018, 240: 189–203
Zhou S, Rabczuk T, Zhuang X. Phase field modeling of quasi-static and dynamic crack propagation: COMSOL implementation and case studies. Advances in Engineering Software, 2018, 122: 31–49
Zhou S, Zhuang X, Zhu H, Rabczuk T. Phase field modelling of crack propagation, branching and coalescence in rocks. Theoretical and Applied Fracture Mechanics, 2018, 96: 174–192
Zhou S, Zhuang X, Rabczuk T. Phase-field modeling of fluid-driven dynamic cracking in porous media. Computer Methods in Applied Mechanics and Engineering, 2019, 350: 169–198
Zhou S, Zhuang X, Rabczuk T. 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, 2019, 355: 729–752
Zhuang X, Zhou S, Sheng M, Li G. On the hydraulic fracturing in naturally-layered porous media using the phase field method. Engineering Geology, 2020, 266: 105306
Acknowledgements
The authors gratefully acknowledge the financial support from ISIRD, SRIC, Indian Institute of Technology Kharagpur (No. IIT/SRIC/CE/PPL/2015-16/108).
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Majumder, M., Chakraborty, D. Bearing and uplift capacities of under-reamed piles in soft clay underlaid by stiff clay using lower-bound finite element limit analysis. Front. Struct. Civ. Eng. 15, 537–551 (2021). https://doi.org/10.1007/s11709-021-0708-x
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DOI: https://doi.org/10.1007/s11709-021-0708-x