Multivariable regression model for Fox depth correction factor

Abstract

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.

Keywords

settlement / embedment / Fox depth correction factor / regression / multivariable

References

[1] Butterfield R, Banerjee P K. A rigid disc embedded in an elastic half space. Geotechnical Engineering, 1971, 2(1): 35–52

[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). 1966

[3] Terzaghi K, Peck R B. Soil Mechanics in Engineering Practices, New York: John Wiley & Sons, 1948

[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, 129–132

[5] Mindlin R D. Force at a point in the interior of a semi-infinite solid. Physics, 1936, 7(5): 195–202

[6] IS 8009. Part 1—Calculation of Settlement of Foundations Subjected to Symmetrical Static Vertical Loads. New Delhi: Bureau of Indian Standards, 1976

[7] The Government of the Hong Kong Special Administrative Region. Hong Kong Code of Practice for Foundations, Building Department. 2004

[8] Bowles J E. Foundation Analysis and Design, 5th ed. New York: McGraw Hill, 1996, 303

[9] Aysen A. Problem Solving in Soil Mechanics. Boca Raton: CRC Press, 2005

[10] Das B M. Principles of Foundation Engineering. 7th ed. Boston: Cengage Learning, 2011

[11] Das B M. Advanced Soil Mechanics. 4th ed. Boca Raton: CRC Press, 2014

[12] Paulos H G, Davis E H. Elastic Solutions for Soil and Rock Mechanics. New York: Wiley, 1973

[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): 77–89

[14] Bowles J E. Elastic foundation settlement on sand deposits. Journal of Geotechnical Engineering, 1987, 113(8): 846–860

[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: 304–313

[16] Ahmed M U. Optimization of footing design by convex simplex algorithm. Thesis of the Master’s Degree. Lubbock: Texas Tech University, 1972

[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: 245–252

[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: 102–108

[19] Pandian N S, Sridharan A, Sathidevi U. Economical consideration of design of combined footings. Indian Geotechnical Journal, 1994, 24(4): 378–409

[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: 1905–1911

[21] Wang Y, Kulhawy F H. Economic design optimization of foundations. Journal of Geotechnical and Geoenvironmental Engineering, 2008, 134(8): 1097–1105

[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): 415–427

RIGHTS & PERMISSIONS

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