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Analysis and Settlement of Partially Stiffened Single and Group of Two Floating Granular Piles

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Abstract

Ground improvement is a technique which a geotechnical engineer normally faces whenever soft soil is encountered. There is a need to look for some economic and feasible option for the provision of foundation in such cases, and one of the option available, is to use the granular pile (GP). The present paper analyzes a single partially stiffened floating and group of two partially stiffened floating GPs. Partial stiffening simply means that the material of the GP is replaced partially in the top region of granular pile by some material, having good mechanical properties i.e. higher deformation modulus e.g. geo-grids, stiffened deep cement mixing, etc. Mathematical formulation and its numerical solution is developed to incorporate the stiffening of granular pile at top portion in the analysis to study its behavior. The effect of stiffening factor i.e. ratio of modulus of deformation of stiffened to un-stiffened portion of GP and percentage length of stiffening i.e. ratio of length of stiffened portion to the total length of the pile are studied on various parameters such as settlement influence factor at top, settlement interaction factor, settlement reduction factor, normalized shear stress distribution along the length of the pile and percentage load transferred to base. As obvious, the settlement influence factor at top decreases with the increase in the stiffening parameters viz. stiffening factor and percentage length of stiffening.

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Abbreviations

GP:

Granular pile

L:

Length of granular pile

n:

Total number of elements of GP

d:

Diameter of granular pile

L/d:

Relative length of GP

P:

Load on each granular pile of two pile group or single GP

Egp :

Deformation modulus of un-stiffened portion of GP

Egpst :

Deformation modulus of stiffened portion of GP

Es :

Deformation modulus of soil

νs and νgp :

Poisson’s Ratio of soil and GP respectively

Kgp = (Egp/Es):

Relative stiffness of granular pile

pb :

Pile base pressure

z:

Depth of granular pile section taken from the top of granular pile

z* (= z/L):

Normalized depth of GP

s:

Spacing between center to center of the piles

s/d:

Normalized spacing center to center between piles

Isp :

Settlement influence factor at top

τ:

Shear stress

τ*2F = τ(πdL)/P:

Normalized shear stresses at various nodes of GP

Ls :

Length of the pile stiffened from the top of the pile

η = Ls/L:

Percentage length of stiffening

χ:

Stiffening factor

ρp :

Normalized displacement of nodes of GP along its length

ρs :

Normalized vertical displacement of soil

Ss :

Vertical soil displacement

α:

Settlement interaction factor for a group of two un-stiffened floating GPs

α2F :

Settlement interaction factor for a group of two partially stiffened floating GPs

β2F :

Settlement reduction factor for a group of two partially stiffened floating GPs

(Pb/P)2F × 100:

Percentage load transferred to the base in a group of two partially stiffened floating GPs

Ispd :

Settlement influence factor for any depth of the GP

[IFs]:

A square matrix for soil displacement influence coefficient

[1IFs] and [2IFs]:

A square matrix for soil displacement influence coefficient for self and adjacent GP respectively

εv and σv :

Axial strain and stress on an element respectively

Pit and Pib :

Axial force on top and bottom of an element respectively

σit and σib :

Axial stresses on top and bottom of an element respectively

σvi :

Average axial stress on the element

MA, MB, MD:

Square matrices

ρt :

Normalized displacement of top node of GP

εv1 :

Axial strain of first element of GP

εvj and εvi :

Axial strain of jth and ith element respectively

εb :

Axial strain of the base of the GP

AMA, AMB:

Square matrices

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Acknowledgements

The author is privileged to express his sincere gratitude to Prof. M.R. Madhav (Civil Engineering Department JNTU, Hyderabad) and Prof. J.K. Sharma (Civil Engineering Department, Rajasthan Technical University, Kota) for his contribution in present work. His high appreciation, positive attitude have played an important role in the outcome of this research work.

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Authors and Affiliations

  1. Rajasthan Technical University, Kota, Rajasthan, India

    Vaibhaw Garg & Jitendra Kumar Sharma

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  1. Vaibhaw Garg
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  2. Jitendra Kumar Sharma
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Correspondence to Vaibhaw Garg.

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Garg, V., Sharma, J.K. Analysis and Settlement of Partially Stiffened Single and Group of Two Floating Granular Piles. Indian Geotech J 49, 191–203 (2019). https://doi.org/10.1007/s40098-018-0321-7

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