Technical Papers
Mar 10, 2012

Calibrated Analytical Formulas for Foundation Model Parameters

Publication: International Journal of Geomechanics
Volume 13, Issue 4

Abstract

A set of analytical formulas for the estimation of foundation model parameters is presented by synthesizing mechanical models at three different levels with corresponding variants of a generalized continuum model presented recently. The generalized continuum model was derived using a unified approach on the basis of a subgrade idealized as an elastic layer of finite thickness overlying a rigid base without making prior simplifying assumptions. The spring stiffness in all variants is inversely proportional to the layer thickness, rendering the model sensitive to this parameter with the potential to yield excessively large deflections for thick formations. This problem is alleviated by eliminating the layer thickness through introduction of a calibration factor in the form of a ratio of the layer thickness to the foundation width. It has been demonstrated that the calibration factor for each model type can be established from comparative analytical-numerical studies. Values obtained in this manner are suggested for practical use. The proposed calibrated formulas have potential applications in routine analysis of beam-like and plate-like shallow foundations and rigid pavements.

Get full access to this article

View all available purchase options and get full access to this article.

References

Avramidis, I. E., and Morfidis, K. (2006). “Bending of beams on three-parameter elastic foundation.” Int. J. Solids Struct., 43, 357–375.
Bowles, J. (1996). Principles of foundation engineering, McGraw Hill, New York.
Brinkgreve, R. B. J., and Broere, W. (2006). Manual of Plaxis 3D Foundation Software Version 1.5, Delft University of Technology and Plaxis bv, Delft, Netherlands.
Colasanti, R. J., and Horvath, J. S. (2010). “Practical subgrade model for improved soil-structure interaction analysis: Software implementation.” Pract. Period. Struct. Des. Constr., 15(4), 278–286.
Das, B. M. (1983). Advanced soil mechanics, McGraw Hill, New York.
Deb, D., Basudhar, P. K., and Chandra, S. (2007). “Generalized model for geosynthetic-reinforced granular fill-soft soil with stone columns.” Int. J. Geomech., 7(4), 266–276.
Filonenko-Borodich, M. M. (1950). “Some approximate theories of elastic foundations.” Uchenyie Zapiski Moskovskogo Gosudarstuennogo Universiteta Mekhanika, Moscow, 46, 3–18.
Hetenyi, M. (1950). “A general solution for the bending of beams on an elastic foundation of arbitrary continuity.” J. Appl. Phys., 21(1), 55–58.
Horvath, J. S. (1983). “Modulus of subgrade reaction: New perspective.” J. Geotech. Engrg., 109(12), 1591–1596.
Horvath, J. S. (2002). Basic SSI concepts and applications overview. Research Rep. CGT-2002-2, Manhattan College School of Engineering, New York.
Horvath, J. S., and Colasanti, R. J. (2011). “Practical subgrade model for improved soil-structure interaction analysis: Model development.” Int. J. Geomech., 11(1), 59–64.
Kerr, A. D. (1964). “Elastic and viscoelastic foundation models.” J. Appl. Mech., 25(80), 491–498.
Kerr, A. D. (1985). “On the determination of foundation model parameters.” J. Geotech. Engrg., 111(11), 1334–1340.
Kerr, A. D., and Rhines, W. J. (1967). “A further study of elastic foundation models.” Rep. S-67-1, New York Univ. School of Engineering and Science, Bronx, NY.
Kim, M., Tutumluer, E., and Kwon, J. (2009). “Nonlinear pavement foundation modeling for three-dimensional finite-element analysis of flexible pavements.” Int. J. Geomech., 9(5), 195–208.
Nogami, T., and O’Neill, M. W. (1985). “Beam on generalized two-parameter foundation.” J. Eng. Mech., 111(5), 664–679.
Pasternak, P. L. (1954). “On a new method of an elastic foundation by means of two foundation constants.” Gosudarstvoennoe Izdatelstvo Literaturi po Stroitelsuve I Arkhitekture, Moscow (in Russian).
Poulos, H. G. (2002). “Calculation of stress and settlement in soil masses.” Geotechnical engineering handbook. Vol. 1: Fundamentals, U. Smoltczyk, ed., Ernst & Sohn, Berlin, 259–312.
Poulos, H. G., and Davis, E. H. (1974). Elastic solutions for soil and rock mechanics, Wiley, New York.
Reissner, E. (1958). “A note on deflections of plates on a viscoelastic foundation.” J. Appl. Mech., 25(80), 144–145.
Selvadurai, A. P. S. (1979). Elastic analysis of soil-foundation interaction, Elsevier Scientific, New York.
Tanahashi, H. (2004). “Formulas for an infinitely long Bernoulli-Euler beam on the Pasternak model.” Soils Found., 44(5), 109–118.
Teferra, A., and Schultze, E. (1988). Formulae, charts and tables in the area of soil mechanics and foundation engineering, Taylor & Francis, London.
Vlasov, V. Z., and Leont’ev, N. N. (1966). Beams, plates, and shells on elastic foundations. Trans. Israel Program for Scientific Translations, Jerusalem.
Wang, H., Tham, L. G., and Cheung, Y. K. (2005). “Beams and plates on elastic foundations: A review.” Prog. Struct. Eng. Mater., 7(4), 174–182.
Winkler, E. (1867). Die Lehre von der Elastizitaet und Festgkeit, H. Dominicus, Prague, Czech Republic (in German).
Worku, A. (2010). “A generalized formulation of continuum models for elastic foundations.” Proc., GeoFlorida 2010: Advances in Analysis, Modeling and Design, ASCE, Reston, VA, 1641–1650.
Worku, A. (2013a). “Discussion of ‘Practical subgrade model for improved soil-structure interaction analysis: Model development’ by J. S. Horvath and R. J. Colasanti.” Int. J. Geomech., 13(1), 97–99.
Worku, A. (2013b). “Discussion of ‘Practical subgrade model for improved soil-structure interaction analysis: Software implementation’ by R. J. Colasanti and J. S. Horvath.” Pract. Period. Struct. Des. Constr., 18(2), 143–144.
Worku, A., and Degu, Y. (2010). “Applications of newly derived and calibrated continuum subgrade models in the analysis of beams on elastic foundations.” Proc., GeoFlorida 2010: Advances in Analysis, Modeling and Design, ASCE, Reston, VA, 1651–1660.
Yamamoto, N., Randolph, M. F., and Einav, I. (2008). “Simple formulas for the response of shallow foundations on compressible sands.” Int. J. Geomech., 8(4), 230–239.
Yin, J.-H. (2000). “Closed-form solution for reinforced Timoshenko beam on elastic foundation.” J. Eng. Mech., 126(8), 868–874.

Information & Authors

Information

Published In

Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 13Issue 4August 2013
Pages: 340 - 347

History

Received: Jan 7, 2011
Accepted: Mar 7, 2012
Published online: Mar 10, 2012
Published in print: Aug 1, 2013

Permissions

Request permissions for this article.

Authors

Affiliations

Asrat Worku, M.ASCE [email protected]
Operations Manager for Geotechnics, Gibb Africa, Ltd., P.O. Box 30020, Harambee Ave., 00100, Nairobi, Kenya; formerly, Associate Professor, Dept. of Civil Engineering, Addis Ababa Univ., Addis Ababa, Ethiopia. E-mail: [email protected]; [email protected]

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.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share