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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2017, Vol. 11 Issue (2) : 228-243     https://doi.org/10.1007/s11709-016-0370-x
RESEARCH ARTICLE |
Linear and nonlinear elastic analysis of closely spaced strip foundations using Pasternak model
Priyanka GHOSH(), S. RAJESH, J. SAI CHAND
Department of Civil Engineering, Indian Institute of Technology, Kanpur, Kanpur 208016, India
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Abstract

In this study, an attempt is made to determine the interaction effect of two closely spaced strip footings using Pasternak model. The study considers small strain problem and has been performed using linear as well as nonlinear elastic analysis to determine the interaction effect of two nearby strip footings. The hyperbolic stress-strain relationship has been considered for the nonlinear elastic analysis. The linear elastic analysis has been carried out by deriving the equations for the interference effect of the footings in the framework of Pasternak model equation; whereas, the nonlinear elastic analysis has been performed using the finite difference method to solve the second order nonlinear differential equation evolved from Pasternak model with proper boundary conditions. Results obtained from the linear and the nonlinear elastic analysis are presented in terms of non-dimensional interaction factors by varying different parameters like width of the foundation, load on the foundation and the depth of the rigid base. Results are suitably compared with the existing values in the literature.

Keywords bearing capacity      linear and non-linear elasticity      foundation      interaction effect      numerical modeling      Pasternak model     
Corresponding Authors: Priyanka GHOSH   
Online First Date: 02 November 2016    Issue Date: 19 May 2017
 Cite this article:   
Priyanka GHOSH,S. RAJESH,J. SAI CHAND. Linear and nonlinear elastic analysis of closely spaced strip foundations using Pasternak model[J]. Front. Struct. Civ. Eng., 2017, 11(2): 228-243.
 URL:  
http://journal.hep.com.cn/fsce/EN/10.1007/s11709-016-0370-x
http://journal.hep.com.cn/fsce/EN/Y2017/V11/I2/228
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Priyanka GHOSH
S. RAJESH
J. SAI CHAND
parametersvalue
modulus of elasticity of the soil medium, E30 MPa
Poisson’s ratio,µ0.30
depth of the rigid base, H/bL2.0 and 4.0
width of the left footing, bL1.0 m
load on the left footing, PL0.20 MN
pressure on the left footing, qL0.20 MPa
load on the right footing, PRnPL
width of the right footing, bRbL
pressure on the right footing, qR(n/a)·qL
a1.0 and 2.0
n/a1.00, 1.25, 1.50, 1.75 and 2.00
Tab.1  Parameters chosen for the analysis []
Fig.1  Problem description sketch
Fig.2  Actual and the idealized conditions of the soil-foundation system. (a) Isolated footing resting on soil medium; (b) proposed soil-foundation system
Fig.3  Idealization for soil – foundation system subjected to line and arbitrary load conditions. (a) Soil medium subjected to line load P per unit length; (b) soil medium subjected to an arbitrary load q(m); (c) isolated strip footing resting on a soil medium; (d) two isolated strip footing resting on a soil medium
Fig.4  Stresses acting on shear layer
Fig.5  Variation of interaction factors with S/bL for linear elastic analysis and symmetric footings (a = 1.0) with (a) H/bL = 2.0, (b) H/bL = 4.0
Fig.6  Variation of interaction factors with S/bL for linear elastic analysis and asymmetric footings (a = 2.0) with (a) H/bL = 2.0, (b)H/bL = 4.0
Fig.7  Variation of interaction factors with S/bL for nonlinear elastic analysis and symmetric footings (a = 1.0) with (a) H/bL = 2.0, (b) H/bL = 4.0
Fig.8  Variation of interaction factors with S/bL for nonlinear elastic analysis and asymmetric footings (a = 2.0) with (a)H/bL = 2.0, (b) H/bL = 4.0
an/aS/bLxLxR
present studyNainegali []present studyNainegali []
1.01.00.51.351.301.361.32
1.01.221.181.251.18
2.01.081.051.121.08
4.01.021.021.030.99
8.01.001.001.001.00
2.00.51.721.611.181.15
1.01.471.421.121.08
2.01.181.141.061.03
4.01.030.981.011.00
8.01.001.001.001.00
2.01.00.51.481.431.161.15
1.01.301.251.091.09
2.01.101.081.041.02
4.01.021.021.020.99
8.01.001.001.001.00
2.00.52.001.881.081.07
1.01.681.581.051.04
2.01.251.201.021.01
4.01.020.961.011.00
8.01.001.001.001.00
Tab.2  Comparison of interaction factors with Nainegali [] for H/bL = 4.0
Fig.9  Comparison of interaction factors obtained from linear and nonlinear elastic analysis for symmetric footings (a = 1.0) with (a) H/bL = 2.0, (b) H/bL = 4.0
Fig.10  Comparison of interaction factors obtained from linear and nonlinear elastic analysis for asymmetric footings (a = 2.0) with (a) H/bL = 2.0, (b) H/bL = 4.0
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