Frontiers of Structural and Civil Engineering

, Volume 11, Issue 2, pp 228–243

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

• Priyanka Ghosh
• S. Rajesh
• J. Sai Chand
Research Article

## 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

## References

1. 1.
Stuart J G. Interference between foundations with special reference to surface footings in sand. Geotechnique, 1962, 12(1): 15–22
2. 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: 214–217Google Scholar
3. 3.
Graham J, Raymond G P, Suppiah A. Bearing capacity of three closely-spaced footings on sand. Geotechnique, 1984, 34(2): 173–181
4. 4.
Kumar J, Ghosh P. Ultimate bearing capacity of two interfering rough strip footings. International Journal of Geomechanics, 2007, 7 (1): 53–62
5. 5.
Kumar A, Saran S. Closely spaced footings on geogrid-reinforced sand. Journal of Geotechnical and Geoenvironmental Engineering, 2003, 129(7): 660–664
6. 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
7. 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
8. 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
9. 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
10. 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
11. 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
12. 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
13. 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
14. 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
15. 15.
Saran S, Agarwal V C. Interference of surface footings in sand. Indian Geotechnical Journal, 1974, 4(2): 129–139Google Scholar
16. 16.
Deshmukh A M. Interaction of different types of footings on sand. Indian Geotechnical Journal, 1979, 9: 193–204Google Scholar
17. 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
18. 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, 34–40Google Scholar
19. 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
20. 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
21. 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
22. 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
23. 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
24. 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
25. 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
26. 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
27. 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
28. 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
29. 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
30. 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
31. 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, 1954Google Scholar
32. 32.
Vlazov V Z, Leontiev U N. Beams, plates and shells on elastic foundations. Israel Program for Scientific Translations, Jerusalem, 1966Google Scholar
33. 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
34. 34.
Timoshenko S P, Goodier J N. Theory of elasticity. 3rd ed. New York: McGraw-Hill, 1970
35. 35.
Selvadurai A P S. Elastic Analysis of Soil Foundation Interaction. Elsevier Scientific Publishing Company, The Netherlands, 1979Google Scholar
36. 36.
Das B M. Principles of Geotechnical Engineering. 5th ed. Thomson Brooks/Cole, India, 2007Google Scholar
37. 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, 2014Google Scholar