Frontiers of Structural and Civil Engineering

, Volume 13, Issue 1, pp 103–109 | Cite as

Multivariable regression model for Fox depth correction factor

  • Ravi Kant MittalEmail author
  • Sanket Rawat
  • Piyush Bansal
Research Article


This paper presents a simple and efficient equation for calculating the Fox depth correction factor used in computation of settlement reduction due to foundation embedment. Classical solution of Boussinesq theory was used originally to develop the Fox depth correction factor equations which were rather complex in nature. The equations were later simplified in the form of graphs and tables and referred in various international code of practices and standard texts for an unsophisticated and quick analysis. However, these tables and graphs provide the factor only for limited values of the input variables and hence again complicates the process of automation of analysis. Therefore, this paper presents a non-linear regression model for the analysis of effect of embedment developed using “IBM Statistical Package for the Social Sciences” software. Through multiple iterations, the value of coefficient of determination is found to reach 0.987. The equation is straightforward, competent and easy to use for both manual and automated calculation of the Fox depth correction factor for wide range of input values. Using the developed equation, parametric study is also conducted in the later part of the paper to analyse the extent of effect of a particular variable on the Fox depth factor.


settlement embedment Fox depth correction factor regression multivariable 


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  1. 1.
    Butterfield R, Banerjee P K. A rigid disc embedded in an elastic half space. Geotechnical Engineering, 1971, 2(1): 35–52Google Scholar
  2. 2.
    Nishida Y. Vertical stress and vertical deformation of ground under a deep circular uniform pressure in the semi-infinite. In: Proceedings of the 1st International Society for Rock Mechanics Congress (ISRM). 1966Google Scholar
  3. 3.
    Terzaghi K, Peck R B. Soil Mechanics in Engineering Practices, New York: John Wiley & Sons, 1948Google Scholar
  4. 4.
    Fox E N. The mean elastic settlement of a uniformly loaded area at a depth below the ground surface. In: Proceedings of the Second International Conference on Soil Mechanics and Foundation Engineering. Rotterdam, 1948, 129–132Google Scholar
  5. 5.
    Mindlin R D. Force at a point in the interior of a semi-infinite solid. Physics, 1936, 7(5): 195–202CrossRefzbMATHGoogle Scholar
  6. 6.
    IS 8009. Part 1—Calculation of Settlement of Foundations Subjected to Symmetrical Static Vertical Loads. New Delhi: Bureau of Indian Standards, 1976Google Scholar
  7. 7.
    The Government of the Hong Kong Special Administrative Region. Hong Kong Code of Practice for Foundations, Building Department. 2004Google Scholar
  8. 8.
    Bowles J E. Foundation Analysis and Design. 5th ed. New York: McGraw Hill, 1996, 303Google Scholar
  9. 9.
    Aysen A. Problem Solving in Soil Mechanics. Boca Raton: CRC Press, 2005Google Scholar
  10. 10.
    Das B M. Principles of Foundation Engineering. 7th ed. Boston: Cengage Learning, 2011Google Scholar
  11. 11.
    Das B M. Advanced Soil Mechanics. 4th ed. Boca Raton: CRC Press, 2014Google Scholar
  12. 12.
    Paulos H G, Davis E H. Elastic Solutions for Soil and Rock Mechanics. New York: Wiley, 1973Google Scholar
  13. 13.
    Shin E C, Das B M. Developments in elastic settlement estimation procedures for shallow foundations on granular soil. KSCE Journal of Civil Engineering, 2011, 15(1): 77–89CrossRefGoogle Scholar
  14. 14.
    Bowles J E. Elastic foundation settlement on sand deposits. Journal of Geotechnical Engineering, 1987, 113(8): 846–860CrossRefGoogle Scholar
  15. 15.
    Hamdia K M, Lahmer T, Nguyen-Thoi T, Rabczuk T. Predicting the fracture toughness of PNCs: A stochastic approach based on ANN and ANFIS. Computational Materials Science, 2015, 102: 304–313CrossRefGoogle Scholar
  16. 16.
    Ahmed M U. Optimization of footing design by convex simplex algorithm. Thesis of the Master’s Degree. Lubbock: Texas Tech University, 1972Google Scholar
  17. 17.
    Bhavikatti S S, Hegde V S. Optimum design of column footing using sequential linear programming. In: Proceedings of the International Conference on Computer Applications in Civil Engineering. Roorkee, 1979, IV: 245–252Google Scholar
  18. 18.
    Desai I D, Desai G D, Desai T B. Cost optimization of isolated sloped footing in granular medium. In: Proceedings of the 2nd International Conference on Computer Aided Analysis and Design in Civil Engineering. Roorkee, 1985, 1: 102–108zbMATHGoogle Scholar
  19. 19.
    Pandian N S, Sridharan A, Sathidevi U. Economical consideration of design of combined footings. Indian Geotechnical Journal, 1994, 24(4): 378–409Google Scholar
  20. 20.
    Basudhar P K, Madanmohan R, Dey A, Deb K, De S. Settlement controlled optimum design of shallow footings. In: Proceedings of the 2nd International Conference on Computational Mechanics and Simulation (ICCMS-06). Guwahati, 2006, II: 1905–1911Google Scholar
  21. 21.
    Wang Y, Kulhawy F H. Economic design optimization of foundations. Journal of Geotechnical and Geoenvironmental Engineering, 2008, 134(8): 1097–1105CrossRefGoogle Scholar
  22. 22.
    Khajehzadeh M, Taha M R, Ahmed E, Eslami M. Modified particle swarm optimization for optimum design of spread footing and retaining wall. Journal of Zhejiang University-Science A (Applied Physics & Engineering), 2011, 12(6): 415–427CrossRefzbMATHGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Ravi Kant Mittal
    • 1
    Email author
  • Sanket Rawat
    • 1
  • Piyush Bansal
    • 2
  1. 1.Department of Civil EngineeringBirla Institute of Technology & SciencePilaniIndia
  2. 2.Department of Civil and Environmental EngineeringVirginia TechBlacksburgUSA

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