Effect of Nonlinear Non-homogeneity of Floating Granular Pile and Soil on Settlement

  • J. K. Sharma
  • Pooja GuptaEmail author
Original Contribution


Ground improvement using granular piles (GPs) is a good alternative to a concrete pile because it increases the load carrying capacity and minimises the settlement of foundations. The present study incorporates the true field conditions with consideration of the nonlinear variation of deformation modulus for GP and soil both. An analytical methodology developed to incorporate nonlinear deformation modulus in pile and soil matrix. Thus, the response of non-homogeneous floating granular pile in non-homogeneous soil is evaluated with respect to settlement influence factor, normalised shear stresses, axial load distribution along granular pile–soil interface and percentage of load transferred to the base to study its true behaviour. An analytical approach based on the continuum is presented in terms of nonlinear variation of deformation modulus of the granular pile and surrounding soil. Formulations for pile elemental displacement equations incorporating linear to nonlinear non-homogeneity parameters, α and δ, for floating granular pile and β and ϒ for non-homogeneous soil are presented. With the increment in relative length of the pile (L/d), the reduction in the magnitude of settlement influence factor further increases. The increase in linear and nonlinear non-homogeneity parameters of soil, β and ϒ, reduces the shear stresses in the upper region of soft soil along with granular pile–soil interface and transfers them to the lower stiffer region of soil.


Granular pile Non-homogeneity Deformation modulus Relative stiffness Shear stresses 



Granular pile

List of symbols


Length of granular pile (metre)


Diameter of GP = (2a) (metre)


Spacing of GPs (metre)


Load on GP (Kn)


Deformation modulus of granular pile material (Kn/m2)


Deformation modulus of soil (Kn/m2)


Poisson’s ratio of soil (dimensionless)


Deformation modulus of soil at base (Kn/m2)


Deformation modulus of soil at surface (Kn/m2)


Relative stiffness of granular pile at base = (Egp/EsL) (dimensionless)


Relative stiffness of granular pile = (Egp0/Es) (dimensionless)


Shear stresses at GP–soil interface (Kn/m2)


Pile base load (Kn)


Total number of elements of GP (dimensionless)


Soil displacements influence factor (dimensionless)


Stress-independent deformation modulus or deformation modulus at the top of granular pile (Kn/m2)


Normalised shear stresses of GP = (τ/(PdL)) (dimensionless)

z* (= z/L)

Normalised depth of GP (dimensionless)


Linear non-homogeneity parameter of granular pile (dimensionless)


Nonlinear non-homogeneity parameter of granular pile (dimensionless)


Linear non-homogeneity parameter of soil (dimensionless)


Nonlinear non-homogeneity parameter of soil (dimensionless)



I am highly indebted and grateful to Professor M.R. Madhav, J.N.T.U. Hyderabad, for his valuable suggestions, His high appreciation and positive attitude about the author’s research ability have played an important role.


  1. 1.
    M.J.V. Baldinelli (1999) A one-dimensional model was used to represent the pile-soil system accounting for soil nonlinearity, slippage at the pile-soil interface and energy dissipation through wave propagation and different types of damping. Ph.D. Thesis, The University of Western Ontario LondonGoogle Scholar
  2. 2.
    D.A. Greenwood, K. Kirsch, Specialist ground improvement by vibratory and dynamic methods—state of the art report, in Proceedings of International Conference on Piling and Ground Treatment for Foundations (Inst. of Civil Engineers, London, 1983), pp. 17–45Google Scholar
  3. 3.
    K.R. Datye, S.S Nagaraju, Installation and testing of rammed stone columns, in Proceedings of IGS Speciality Session, 5th ARC on SMFE, Bangalore (1975), pp. 101–104Google Scholar
  4. 4.
    H. Aboshi, E. Ichimoto, M. Enoki, K. Harda, The composer—a method to improve characteristics of soft clays by inclusion of large diameter sand columns, in Proceedings of International Conference on Soil Reinforcement: Reinforced Earth and Other Techniques, Paris, vol. 1 (1979), pp. 211–216Google Scholar
  5. 5.
    B. Vidyaranya, M.R. Madhav, M. Kumar, Effect of non-homogenous ground on ultimate pullout capacity of GPA, in Proceedings of IGC-2010, GEOtrendz December 16–18, 2010 IGS Mumbai Chapter & IIT Bombay (2010), pp. 965–968Google Scholar
  6. 6.
    M.R. Madhav, J.K. Sharma, S. Chandra, Analysis and settlement of a non-homogeneous granular pile. Indian Geotech. J. 36(3), 249–271 (2006)Google Scholar
  7. 7.
    P. Gupta, J.K. Sharma, Settlement analysis of non-homogeneous single granular pile. Indian Geotech. J. 48(1), 92–101 (2018)CrossRefGoogle Scholar
  8. 8.
    K. Rajyalakshmi, K. Ramu, Bearing capacity of reinforced granular beds on soft non-homogeneous clay. Int. J. Eng. Sci. Technol. 3(7), 5851–5859 (2011)Google Scholar
  9. 9.
    J. Nakayama, I. Eizabuno, K. Hideo, T. Soichi, On stabilisation characteristics of sand compaction piles. JSSMFE 13(3), 61–68 (1973)Google Scholar
  10. 10.
    Y. Shamoto, Y. Katsura, T. Katsuyuki, J.M. Zhang, A simplified method for evaluating the effectiveness of compaction piles in sands containing fines. JSSMFE 37(1), 89–96 (1997)Google Scholar
  11. 11.
    S. Valliappan, I.K. Lee, P. Boonlualohr, Settlement analysis of pile in layered soil. in Proceedings of 7th Biennial Conference of the Australian Road Research Board, Adelaide, Australia, vol 7, Part 7 (1974), pp. 144–153Google Scholar
  12. 12.
    P.K. Banerjee, T.G. Davies, Analysis of pile groups embedded in Gibson soil, in Proceedings of 9th International Conference on Soil Mechanics and Foundation Engineering, Tokyo, Japan, vol 1 (1977), pp. 381–386Google Scholar
  13. 13.
    H.G. Poulos, Settlement of single piles in non-homogeneous soil. J. Geotech. Eng. Div. ASCE 105(GT5), 627–641 (1979)Google Scholar
  14. 14.
    K.D.S. Grover, J.K. Sharma, M.R. Madhav, Settlement analysis of single granular pile with stiffened top. Int. J. Sci. Eng. Res. 6(6), 61–75 (2015)Google Scholar
  15. 15.
    R.D. Mindlin, Force at a point in the interior of a semi-infinite solid. J. Appl. Phys. 7(5), 195–202 (1936)zbMATHGoogle Scholar
  16. 16.
    H.G. Poulos, N.S. Mattes, The behaviour of axially-loaded end- bearing piles. Geotechnique 19, 285–300 (1969)CrossRefGoogle Scholar
  17. 17.
    M.R. Madhav, J.K. Sharma, S. Chandra, Analysis and settlement of a non-homogeneous granular pile. Indian Geotech. J. 36(3), 249–271 (2006)Google Scholar
  18. 18.
    M.R. Madhav, J.K. Sharma, V. Sivakumar, Settlement and load distribution in a granular piled raft. Geomech. Eng. 1(1), 97–112 (2009)CrossRefGoogle Scholar

Copyright information

© The Institution of Engineers (India) 2018

Authors and Affiliations

  1. 1.Civil Engineering DepartmentRajasthan Technical UniversityKotaIndia
  2. 2.KotaIndia

Personalised recommendations