Geotechnical and Geological Engineering

, Volume 36, Issue 5, pp 3029–3080 | Cite as

Ultimate Bearing Capacity Prediction of Eccentrically Inclined Loaded Strip Footings

  • Rabi Narayan Behera
  • Chittaranjan Patra
Original paper


Extensive laboratory model tests have been carried out on a strip footing resting over dry sand bed subjected to eccentrically inclined load to determine the ultimate bearing capacity (Patra et al. in Int J Geotech Eng 6(3):343–352, 2012a., Int J Geotech Eng 6(4):507–514, b. Similarly, lower bound calculations based on finite element method were performed to compute the bearing capacity of a strip footing subjected to an eccentric and inclined load lying over a cohesionless soil with varying embedment depth and relative density (Krabbenhoft et al. in Int J Geomech ASCE, 2014. The load may be applied in two ways namely, towards the center line and away from the center line of the footing. Based on the results (both experimental and numerical analyses), a neural network model is developed to predict the reduction factor that will be used in computing the ultimate bearing capacity of an eccentrically inclined loaded strip footing. This reduction factor (RF) is the ratio of the ultimate bearing capacity of the footing subjected to an eccentrically inclined load to the ultimate bearing capacity of the footing subjected to a centric vertical load. A thorough sensitivity analysis is carried out to evaluate the parameters affecting the reduction factor. Based on the weights of the developed neural network model, a neural interpretation diagram is developed to find out whether the input parameters have direct or inverse effect on the output. A prediction model equation is framed with the trained weights of the neural network as the model parameters. The predictions from ANN, and those from other approaches, are compared with the results computed from both experimentation and FEM analyses. The ANN model results are found to be more accurate and well matched with other results.


Eccentrically inclined load Partially compensated Reinforced Ultimate bearing capacity Reduction factor Neural network 


  1. Das SK, Basudhar PK (2006) Undrained lateral load capacity of piles in clay using artificial neural network. Comput Geotech 33(8):454–459. CrossRefGoogle Scholar
  2. Dubrova GA (1973) Interaction of Soils and Structures. Rechnoy Transport, MoscowGoogle Scholar
  3. Fedorovskii VG (2003) Bearing capacity of eccentrically and obliquely loaded strip foundation on a weightless cohesive bed. Soil Mech Found Eng 40(3):161–172CrossRefGoogle Scholar
  4. Fedorovskii VG (2005) Bearing capacity of the granular bed of a strip foundation under an inclined eccentric load. Soil Mech Found Eng 42(4):111–119CrossRefGoogle Scholar
  5. Ganesh R, Khuntia S, Sahoo J (2016) Bearing capacity of shallow strip foundations in sand under eccentric and oblique loads. Int J Geomech ASCE. Google Scholar
  6. Garson GD (1991) Interpreting neural-network connection weights. Artif Intel Exp 6(7):47–51Google Scholar
  7. Goh ATC (1995) Back-propagation neural networks for modeling complex systems. Artif Intell Eng 9:143–151. CrossRefGoogle Scholar
  8. Goh ATC, Kulhawy FH, Chua CG (2005) Bayesian neural network analysis of undrained side resistance of drilled shafts. J Geotech Geoenviorn Eng 131(1):84–93. CrossRefGoogle Scholar
  9. Gottardi G, Butterfield R (1993) On the bearing capacity of surface footings on sand under general planar loads. Soils Found 33(3):68–79CrossRefGoogle Scholar
  10. Gourvenec S, Govoni L, Gottardi G (2008) An investigation of shallow foundations on sand under moment loading. In: Brown MJ, Bransby MF, Brennan AJ, Knappett JA (eds) Proceedings of 2nd BGA international conference on foundations, ICOF2008. IHS BRE Press, Bracknell, pp 873–884Google Scholar
  11. Guyon I, Elisseeff A (2003) An Introduction to variable and feature selection. J MachLearn Res 3:1157–1182Google Scholar
  12. Hansen JB (1970) A revised and extended formula for bearing capacity. Dan Geotech Inst Bull 28:5–11Google Scholar
  13. Hjiaj M, Lyamin AV, Sloan SW (2004) Bearing capacity of a cohesive-frictional soil under non-eccentric inclined loading. Comput Geotech 31:491–516CrossRefGoogle Scholar
  14. Krabbenhoft S, Damkilde L, Krabbenhoft K (2012) Lower bound calculations of the bearing capacity of eccentrically loaded footings in cohesionless soil. Can Geotech J 49(3):298–310. CrossRefGoogle Scholar
  15. Krabbenhoft S, Damkilde L, Krabbenhoft K (2014) Bearing capacity of strip footings in cohesionless soil subject to eccentric and inclined loads. Int J Geomech ASCE. Google Scholar
  16. Loukidis D, Chakraborty T, Salgado R (2008) Bearing capacity of strip footings on purely frictional soil under eccentric and inclined loads. Can Geotech 45(6):768–787. CrossRefGoogle Scholar
  17. Meyerhof GG (1953) The bearing capacity of foundations under eccentric and inclined loads. In: Proceedings of the 3rd international conference on soil mechanics and foundation engineering (ICSMFE), Zurich, vol 1, pp. 440–445Google Scholar
  18. Meyerhof GG (1963) Some recent research on the bearing capacity of foundations. Can Geotech 1(1):16–26CrossRefGoogle Scholar
  19. Meyerhof GG, Koumoto T (1987) Inclination factors for bearing capacity of shallow footings. J Geotech Eng ASCE 113(9):1013–1018CrossRefGoogle Scholar
  20. Michalowski RL, You L (1998) Effective width rule in calculations of bearing capacity of shallow footings. Comp Geotech 23:237–253CrossRefGoogle Scholar
  21. Muhs H, Weiss K (1973) Inclined load tests on shallow strip footing. In: Proceedings of 8th international conference on soil mechanics and foundation engineering (ICSMFE), Moscow, 1.3Google Scholar
  22. Okamura M, Mihara A, Takemura J (2002) Effects of footing size and aspect ratio on the bearing capacity of sand subjected to eccentric loading. Soils Found 42(4):43–56CrossRefGoogle Scholar
  23. Olden JD, Joy MK, Death RG (2004) An accurate comparison of methods for quantifying variable importance in artificial neural networks using simulated data. Eco Model 178:389–397. CrossRefGoogle Scholar
  24. Ornek M (2014) Estimation of ultimate loads of eccentric-inclined loaded strip footings rested on sandy soils. Neural Comput Appl 25(1):39–54CrossRefGoogle Scholar
  25. Ozesmi SL, Ozesmi U (1999) An artificial neural network approach to spatial modeling with inter specific interactions. Eco Model 116:15–31. CrossRefGoogle Scholar
  26. Patra CR, Behera RN, Sivakugan N, Das BM (2012a) Ultimate bearing capacity of shallow strip foundation under eccentrically inclined load: part I. Int J Geotech Eng 6(3):343–352. CrossRefGoogle Scholar
  27. Patra CR, Behera RN, Sivakugan N, Das BM (2012b) Ultimate bearing capacity of shallow strip foundation under eccentrically inclined load: part II. Int J Geotech Eng 6(4):507–514. CrossRefGoogle Scholar
  28. Patra CR, Sivakugan N, Das BM (2016) Recent developments on bearing capacity of strip foundation on granular soil under eccentrically inclined load. Int J Geotech Eng 10(1):31–39. CrossRefGoogle Scholar
  29. Perloff WH, Barron W (1976) Soil Mechanics: Principles and Applications. Ronald Press, New YorkGoogle Scholar
  30. Prakash S, Saran S (1971) Bearing capacity of eccentrically loaded footings. J Soil Mech Found Div ASCE 97(1):95–117Google Scholar
  31. Purkayastha RD, Char RAN (1977) Stability analysis for eccentrically loaded footings. J Geotech Eng Div ASCE 103(6):647–651Google Scholar
  32. Saran S, Agarwal RK (1991) Bearing capacity of eccentrically obliquely loaded foundation. J Geotech Eng 117(11):1669–1690CrossRefGoogle Scholar
  33. Saran S, Prakash S, Murty AVSR (1971) Bearing capacity of footings under inclined loads. Soils Found 11(1):47–52CrossRefGoogle Scholar
  34. Sastry VVRN, Meyerhof GG (1987) Inclination factors for strip footings. J Geotech Eng ASCE 113(5):524–527CrossRefGoogle Scholar
  35. Shahin MA, Jaksa MB, Maier HR (2008) State-of-the-art of artificial neural networks in geotechnical engineering. Elect J Geotech Eng., ISSN: 1089-3032
  36. Tang C, Phoon K, Toh K (2015) Effect of footing width on N γ and failure envelope of eccentrically and obliquely loaded strip footings on sand. Can Geotech J 52(6):694–707CrossRefGoogle Scholar
  37. Vesic AS (1975) Bearing capacity of shallow foundations. In: Winterkorn HF, Fang H-Y (eds) Foundation Engineering Handbook. Van Nostrand Reinhold, New York, pp 121–147Google Scholar
  38. Viladkar MN, Zedan AJ, Saran S (2013) Non-dimensional correlations for design of eccentrically obliquely loaded footings on cohesionless soils. Int J Geotech Eng 7(4):333–345. CrossRefGoogle Scholar
  39. Wilby RL, Abrahart RJ, Dawson CW (2003) Detection of conceptual model rainfall-runoff processes inside an artificial neural network. Hydro Sci J 48(2):163–181. CrossRefGoogle Scholar
  40. Yahia-Cherif H, Mabrouki A, Benmeddour D, Mellas M (2017) Bearing capacity of embedded strip footings on cohesionless soil under vertical and horizontal loads. Geotech Geol Eng 35:547–558CrossRefGoogle Scholar
  41. Zdravkovic L, Ng PM, Potts DM (2002) Bearing capacity of surface foundations on sand subjected to combined loading. Numerical methods in geotechnical engineering, Philippe Mestat, ed., Presses de l’ENPC/LCPC, ParisGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil EngineeringNational Institute of Technology RourkelaRourkelaIndia

Personalised recommendations