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Linear and nonlinear elastic analysis of closely spaced strip foundations using Pasternak model

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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.

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References

  1. Stuart J G. Interference between foundations with special reference to surface footings in sand. Geotechnique, 1962, 12(1): 15–22

    Article  Google Scholar 

  2. West J M, Stuart J G. Oblique loading resulting from interference between surface footings on sand. In: Proceedings of the 6th International Conference on Soil Mechanics. Montreal, 1965, 2: 214–217

    Google Scholar 

  3. Graham J, Raymond G P, Suppiah A. Bearing capacity of three closely-spaced footings on sand. Geotechnique, 1984, 34(2): 173–181

    Article  Google Scholar 

  4. Kumar J, Ghosh P. Ultimate bearing capacity of two interfering rough strip footings. International Journal of Geomechanics, 2007, 7 (1): 53–62

    Article  Google Scholar 

  5. Kumar A, Saran S. Closely spaced footings on geogrid-reinforced sand. Journal of Geotechnical and Geoenvironmental Engineering, 2003, 129(7): 660–664

    Article  Google Scholar 

  6. Griffiths D V, Fenton G A, Manoharan N. Undrained bearing capacity of two-strip footings on spatially random soil. International Journal of Geomechanics, 2006, 6(6): 421–427

    Article  Google Scholar 

  7. Kumar J, Ghosh P. Upper bound limit analysis for finding interference effect of two nearby strip footings on sand. Geotechnical and Geological Engineering, 2007, 25(5): 499–507

    Article  Google Scholar 

  8. Kumar J, Kouzer K M. Bearing capacity of two interfering footings. International Journal for Numerical and Analytical Methods in Geomechanics, 2008, 32(3): 251–264

    Article  MATH  Google Scholar 

  9. Kouzer K M, Kumar J. Ultimate bearing capacity of a footing considering the interference of an existing footing on sand. Geotechnical and Geological Engineering, 2010, 28(4): 457–470

    Article  Google Scholar 

  10. Kumar J, Bhattacharya P. Bearing capacity of two interfering strip footings from lower bound finite elements limit analysis. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37(5): 441–452

    Article  Google Scholar 

  11. Mabrouki A, Benmeddour D, Frank R, Mellas M. Numerical study of the bearing capacity for two interfering strip footings on sands. Computers and Geotechnics, 2010, 37(4): 431–439

    Article  Google Scholar 

  12. Ghosh P, Sharma A. Interference effect of two nearby strip footings on layered soil: theory of elasticity approach. Acta Geotechnica, 2010, 5(3): 189–198

    Article  Google Scholar 

  13. Lee J, Eun J, Prezzi M, Salgado R. Strain influence diagrams for settlement estimation of both isolated and multiple footings in sand. Journal of Geotechnical and Geoenvironmental Engineering, 2008, 134(4): 417–427

    Article  Google Scholar 

  14. Nainegali L S, Basudhar P K, Ghosh P. Interference of two asymmetric closely spaced strip footings resting on nonhomogeneous and linearly elastic soil bed. International Journal of Geomechanics, 2013, 13(6): 840–851

    Article  Google Scholar 

  15. Saran S, Agarwal V C. Interference of surface footings in sand. Indian Geotechnical Journal, 1974, 4(2): 129–139

    Google Scholar 

  16. Deshmukh A M. Interaction of different types of footings on sand. Indian Geotechnical Journal, 1979, 9: 193–204

    Google Scholar 

  17. Das B M, Larbi-Cherif S. Bearing capacity of two closely spaced shallow foundations on sand. Soil and Foundation, 1983, 23(1): 1–7

    Article  Google Scholar 

  18. Das B M, Puri V K, Neo B K. Interference effects between two surface footings on layered soil. Transportation Research Record 1406, Transportation Research Board, Washington, DC, 1993, 34–40

    Google Scholar 

  19. Kumar J, Bhoi M K. Interference of two closely spaced strip footings on sand using model tests. Journal of Geotechnical and Geoenvironmental Engineering, 2009, 135(4): 595–604

    Article  Google Scholar 

  20. Ghosh P, Kumar S R. Interference effect of two nearby strip surface footings on cohesionless layered soil. International Journal of Geotechnical Engineering, 2011, 5(1): 87–94

    Article  Google Scholar 

  21. Srinivasan V, Ghosh P. Experimental investigation on interaction problem of two nearby circular footings on layered cohesionless soil. Geomechanics and Geoengineering, 2013, 8(2): 97–106

    Article  Google Scholar 

  22. Rabczuk T, Belytschko T. A three dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799

    Article  MathSciNet  MATH  Google Scholar 

  23. 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

    Article  MATH  Google Scholar 

  24. Areias P, Rabczuk T, Dias-da-Costa D. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 2013, 110: 113–137

    Article  Google Scholar 

  25. Nguyen-Xuan H, Liu G R, Bordas S, Natarajan S, Rabczuk T. An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order. Computer Methods in Applied Mechanics and Engineering, 2013, 253: 252–273

    Article  MathSciNet  MATH  Google Scholar 

  26. Amiri F, Anitescu C, Arroyo M, Bordas S P A, Rabczuk T. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics, 2014, 53(1): 45–57

    Article  MathSciNet  MATH  Google Scholar 

  27. Areias P, Rabczuk T, Camanho P P. Finite strain fracture of 2D problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics, 2014, 72: 50–63

    Article  Google Scholar 

  28. Nguyen-Xuan H, Liu G R. An edge-based finite element method (ES-FEM) with adaptive scaled-bubble functions for plane strain limit analysis. Computer Methods in Applied Mechanics and Engineering, 2015, 285: 877–905

    Article  MathSciNet  MATH  Google Scholar 

  29. Nguyen-Xuan H, Rabczuk T. Adaptive selective ES-FEM limit analysis of cracked plane-strain structures. Frontiers in Civil Engineering, 2015, 9(4): 478–490

    Article  Google Scholar 

  30. Nguyen-Xuan H, Wu C T, Liu G R. An adaptive selective ES-FEM for plastic collapse analysis. European Journal of Mechanics. A, Solids, 2016, 58: 278–290

    Article  MathSciNet  MATH  Google Scholar 

  31. Pasternak P L. On a new method of analysis of an elastic foundation by means of two foundation constants. Gosudarstvennoe Izdatelstro Liberaturi po Stroitelstvui Arkhitekture, Moscow, 1954

    Google Scholar 

  32. Vlazov V Z, Leontiev U N. Beams, plates and shells on elastic foundations. Israel Program for Scientific Translations, Jerusalem, 1966

    Google Scholar 

  33. Konder R L, Zelasko J S. Void ratio effects on the hyperbolic stress strain response of a sand. Canadian Geotechnical Journal, 1963, 2 (1): 40–52

    Article  Google Scholar 

  34. Timoshenko S P, Goodier J N. Theory of elasticity. 3rd ed. New York: McGraw-Hill, 1970

    MATH  Google Scholar 

  35. Selvadurai A P S. Elastic Analysis of Soil Foundation Interaction. Elsevier Scientific Publishing Company, The Netherlands, 1979

    Google Scholar 

  36. Das B M. Principles of Geotechnical Engineering. 5th ed. Thomson Brooks/Cole, India, 2007

    Google Scholar 

  37. Nainegali L S. Finite element analysis of two symmetric and asymmetric interfering footings resting on linearly and non-linearly elastic foundation beds. Dissertation for the Doctoral Degree, IIT Kanpur, 2014

    Google Scholar 

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Correspondence to Priyanka Ghosh.

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Ghosh, P., Rajesh, S. & Sai Chand, J. Linear and nonlinear elastic analysis of closely spaced strip foundations using Pasternak model. Front. Struct. Civ. Eng. 11, 228–243 (2017). https://doi.org/10.1007/s11709-016-0370-x

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  • DOI: https://doi.org/10.1007/s11709-016-0370-x

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