Complete Analytical Solution for Linear Soil Pressure Distribution under Rigid Rectangular Spread Footings
Publication: International Journal of Geomechanics
Volume 17, Issue 7
Abstract
The main objective of this paper is to establish a complete analytical solution concerning the linear pressure distribution under rigid rectangular spread footings. An eccentricity diagram is developed to map the unique footing deformations and compression zones in each one of five distinct regions. For each region, the linear soil pressure, neutral axis position, and pressure values at the four corners are expressed in closed forms. The accuracy and consistency of the explicit expressions are verified by presenting several special boundary cases, whereas the physical interpretation is brought out by analyzing the eccentricity diagram. A generic nomogram providing the maximum soil pressure is also formed to promote efficient structural footing design. The developed analytical formulas for responses and resultants enable algorithmic implications without iterations and offer high computational efficiency. Proper examples, generated via developed computer software, exhibit how the theoretical content of this article is applied in practice. The software enables three-dimensional (3D) viewing of the deformed and undeformed physical and mathematical model of the structure, allowing detailed visual inspection of the results.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work concerns part of the research activities associated with the development of integrated engineering software, produced on behalf of pi-Systems International S.A. (Athens, Greece). The authors express their appreciation to the company for the financial support provided, the Institute of Structural Analysis and Seismic Research of National Technical University of Athens for the contribution in developing the computational algorithms for the space-frame model, and all other associates involved.
References
Algin, H. M. (1996). “The behavior of flexibly bedded concrete paver pavements.” Ph.D. thesis, Univ. of Newcastle upon Tyne, Newcastle upon Tyne, U.K.
Algin, H. M. (2000). “Stresses from linearly distributed pressures over rectangular areas.” Int. J. Numer. Anal. Methods Geomech., 24(8), 681–692.
Algin, H. M. (2007a). “Interlock mechanism of concrete block pavements.” J. Transp. Eng., 318–326.
Algin, H. M. (2007b). “Practical formula for dimensioning a rectangular footing.” Eng. Struct., 29(6), 1128–1134.
Algin, H. (2009). “Elastic settlement under eccentrically loaded rectangular surface footings on sand deposits.” J. Geotech. Geoenviron. Eng., 1499–1508.
Bowles, J. E. (1977). Foundation analysis and design, 3rd Ed., McGraw Hill, New York.
CEN (European Committee for Standardization). (2002). Eurocode 1: Actions on structures—Part 1-1: General actions—Densities, self-weight, imposed loads for buildings, Brussels, Belgium.
CEN (European Committee for Standardization). (2004a). Eurocode 2: Design of concrete structures—Part 1-1: General rules and rules for buildings, Brussels, Belgium.
CEN (European Committee for Standardization). (2004b). Eurocode 7: Geotechnical design—Part 1: General rules, Brussels, Belgium.
CEN (European Committee for Standardization). (2004c). Eurocode 8: Design of structures for earthquake resistance—Part 1: General rules, seismic actions and rules for buildings, Brussels, Belgium.
Highter, W. H., and Anders, J. C. (1985). “Dimensioning footings subjected to eccentric loads.” J. Geotech. Engrg., 659–665.
Irles, R., and Irles, F. (1994). “Explicit stresses under rectangular footings.” J. Geotech. Engrg., 444–450.
Ivan, A. (2010). “Pressures distribution for eccentrically loaded rectangular footings on elastic soils.” Proc., Int. Conf. on Mathematical Models for Engineering Science, World Scientific and Engineering Academy and Society, Stevens Point, WI, 213–216.
Jarquio, R., and Jarquio, V. (1983). “Design footing area with biaxial bending.” J. Geotech. Engrg., 1337–1341.
Kameswara Rao, N. S. V. (2011). “Analysis of footings on elastic foundations.” Foundation design: Theory and practice, Chaper 5, John Wiley & Sons (Asia) Pte Ltd., Singapore.
Konstantinides, A., and Bellos, J. (2013). Earthquake resistant buildings made of reinforced concrete: Static and dynamic analysis according to Eurocodes, Vol. B, Alta Grafico, Athens, Greece.
Özmen, G. (2011). “Determination of base stresses in rectangular footings under biaxial bending.” Teknik Dergi, 22, 5659–5674.
Rayhani, M. H. T., and El Naggar, M. H. (2008). “Numerical modeling of seismic response of rigid foundation on soft soil.” Int. J. Geomech., 336–346.
Rodriguez-Gutierrez, J. A., and Aristizabal-Ochoa, J. D. (2013). “Rigid spread footings resting on soil subjected to axial load and biaxial bending. I: Simplified analytical method.” Int. J. Geomech., 109–119.
Rojas, A. L., Herrera, J. G. F., Vallejo, R. A. A., and Alvarez, M. A. C. (2013). “Design of isolated footings of rectangular form using a new model.” Int. J. Innovative Comput. Inf. Control, 9(10), 4001–4021.
Smith-Pardo, J. P., and Bobet, A. (2007). “Behavior of rigid footings on gravel under axial load and moment.” J. Geotech. Geoenviron. Eng., 1203–1215.
Vitone, D. M., and Valsangkar, A. J. (1986). “Stresses from loads over rectangular areas.” J. Geotech. Engrg., 961–964.
Yamamoto, N., Randolph, M. F., and Einav, I. (2008). “Simple formulas for the response of shallow foundations on compressible sands.” Int. J. Geomech., 230–239.
Information & Authors
Information
Published In
Copyright
© 2017 American Society of Civil Engineers.
History
Received: Aug 3, 2016
Accepted: Nov 2, 2016
Published online: Jan 13, 2017
Discussion open until: Jun 13, 2017
Published in print: Jul 1, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.