Frontiers of Structural and Civil Engineering

, Volume 13, Issue 1, pp 103–109

# Multivariable regression model for Fox depth correction factor

• Ravi Kant Mittal
• Sanket Rawat
• Piyush Bansal
Research Article

## 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

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© 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