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Reinforcement Effect on the Static Analysis of Circular Footing Resting over Winkler Elastic Foundation

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Abstract

This paper pertains to the development of a lumped parameter model for predicting the flexural response of a circular footing resting on an engineered reinforced soil bed. The bed is constructed by placing a smooth circular geo-mat over the natural loose sand deposit on which a compacted sand fill is placed. The dense and the loose sand strata are idealized with Winkler springs of different stiffness values. Considering the problem to be axi-symmetric the resulting governing differential equations have been derived and solved for appropriate boundary and continuity conditions by using finite difference technique. Effects of the different parameters like the ratio of flexural rigidity and the dimensions of the footing and the reinforcing element, the ratio of stiffness of the upper and the lower sand layers, and the placement depth of the reinforcement on the settlement and flexural response of the footing have been presented.

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Abbreviations

Dt :

Flexural rigidity of upper plate

Db :

Flexural rigidity of lower plate

h:

Depth of placement of lower plate (m)

h′:

Normalized depth of placement of lower plate (dimensionless)

k1 :

Modulus of subgrade reaction of upper layer soil (N/m3)

k2 :

Modulus of subgrade reaction of lower layer soil (N/m3)

rt :

Radius of upper plate (m)

rb :

Radius of lower plate (m)

P:

Point load (N)

R:

Relative flexural rigidity of plates (Dt/Db) (nondimensional)

R1 :

Characteristic length of upper plate (= \(\sqrt[4]{{D_{t} /k_{1} }}\))

R2 :

Characteristic length of upper plate (= \(\sqrt[4]{{D_{b} /k_{1} }}\))

K:

Relative stiffness of soils (k1/k2)

r:

Radial distance

yt :

Deflection of upper plate

yb :

Deflection of lower plate

y′t :

Normalized deflection of upper plate (dimensionless)

y′b :

Normalized deflection of lower plate (dimensionless)

z:

Normalized radial distance (dimensionless)

z1 :

Normalized radius of upper plate (dimensionless)

z2 :

Normalized radius of lower plate (dimensionless)

zr :

Ratio of radius of upper and lower plates (dimensionless)

γ 1 :

Unit weight of upper soil (N/m3)

γ 2 :

Unit weight of lower soil (N/m3)

\(\gamma '_{1}\) :

Normalized unit weight of upper soil

υ :

Poisons ratio of upper plate

υ 1 :

Poisons ratio of lower plate

m:

Number of elements in centrally distributed load region in zone I

n:

Number of elements in upper and lower plates in zone II

q:

Number of elements in lower plate in zone III

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Authors and Affiliations

  1. Acellent Technologies Inc., Sunnyvale, CA, 94085, USA

    Susheel K. Yadav

  2. Department of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson, AZ, 85721, USA

    Umar Amjad

  3. Department of Civil Engineering, Indian Institute of Technology, Kanpur, 208016, India

    Prabir K. Basudhar

Authors
  1. Susheel K. Yadav
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  2. Umar Amjad
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  3. Prabir K. Basudhar
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Correspondence to Susheel K. Yadav.

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Yadav, S.K., Amjad, U. & Basudhar, P.K. Reinforcement Effect on the Static Analysis of Circular Footing Resting over Winkler Elastic Foundation. Geotech Geol Eng 36, 3665–3681 (2018). https://doi.org/10.1007/s10706-018-0564-1

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  • DOI: https://doi.org/10.1007/s10706-018-0564-1

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