Abstract
The paper pertains to the development of a new relationship expressing the Winkler modulus of subgrade reaction as a function of elastic parameters such as the modulus of elasticity and Poisson’s ratio of the foundation soil, and the relative rigidity of the foundation soil and the beam resting over the same. It ensures that the maximum values of beam deflection and bending moment computed by using both the theory of elastic continuum and lumped parameter modeling are either identical or very close to each other. In this respect the developed expression can be construed to be superior to those proposed by Biot and Vesic, which respectively predict correct values for only one of the quantities (either maximum bending moment or maximum deflection). In addition, the proposed model for subgrade modulus is applicable to multiple load conditions as well unlike the other two approaches as reported.
Similar content being viewed by others
References
Albet P, Kovacs M (2003) Periodica Polytechnica Ser. Civ Eng 42(2):169–174
Allotey N, El Nagger MH (2008) Generalized dynamic Winkler model for nonlinear soil–structure interaction analysis. Can Geotech J 45:560–573
Biot MA (1937) Bending of an infinite beam on an elastic foundation. J Appl Mech (Trans ASME) 4:A1–A7
Boulanger RW, Curras CJ, Kutter BL, Wilson DW, Abghari A (1999) A seismic soil-pile-structure interaction experiments and analysis. J Geotech Geoenvironm Eng 125:750–759
Bowels JE (2001) Foundation analysis and design. McGraw Hill, New York
Brown PT (1973) Strip footings with concentrated loads on deep elastic foundations. University of Sydney, School of Civil Engineering
Chandrasekaran VS (2001) Numerical and centrifuge modelling in soil structure interaction. Indian Geotech J 31(1):1–59
Daloglu AT, Vallabhan CVG (2000) Values of k for slab on winkler foundation. J Geotech Geoenvironm Eng ASCE 126(5):463–471
Dey A (2009) Nonlinearly elastic and viscoelastic, unreinforced and reinforced foundation beds: modeling and model parameter estimation. Ph.D. thesis, Department of Civil Engineering, Indian Institute of Technology Kanpur, India
Fox RL (1971) Optimization methods for engineering design. Addison-Wesley, Reading, MA
Hetenyi M (1946) Beams on elastic foundation. University of Michigan Press, Ann Arbor
Iskander GM, Gabr RH (2009) Soil-pipe interaction due to tunneling: comparision between Winkler and elastic continuum solutions, internet
Kerr MG (1965) The mechanical effects of the gravid uterus in late pregnancy. BJOG Int J Obstet Gynaecol 72(4):513–529
Klar A, Vorster TEB, Soga K, Mair RJ (2004) Soil-pipe-tunnel interaction: comparisonbetween winkler and elastic continuum solutions. Department of Engineering, University of Cambridge, UK, pp 1–14
Madhav MR, Poorooshasb HB (1989) Modified Pasternak model for reinforced soil. Math Comput Model 12(12):1505–1509
Morgenstern NR, Price VE (1967) A numerical method for solving the equations of stability of general slip surfaces. Comput J 9(4):388–393
Prendergast LJ, Gavin K (2016) A comparison of initial stiffness formulations for small-strain soil–pile dynamic Winkler modelling. Soil Dyn Earthq Eng 81:27–41
Sadrekarimi J, Akbarzad M (2009) Comparative study of methods of determination of coefficient of subgrade reaction. Electron J Geotech Eng 14(s1–6):45–61
Sall OA, Fall M, Berthaud Y, Ba M (2013) Influence of the elastic modulus of the soil and concrete foundation on displacements of a mat foundation. Open J Civ Eng 3:228–233
Scott RF (1981) Foundation analysis, vol 07632. Prentice–Hall Inc, Englewood Cliffs, pp 141–150
Selvadurai APS (1979) Elastic analysis of soil-foundation interaction development in geotechnical engineering, vol 17. Elsevier, Amsterdam
Shukla SK, Chandra S (1994) Generalized mechanical model for geosynthetic-reinforced foundation soil. Geotext Geomembr 13:813–825
Smith GN, Pole EL (1980) Elements of foundation design. Granada Publishing Limited-Technical Books Division, London
Terzaghi K (1955) Evalution of conefficients of subgrade reaction. Geotechnique 5(4):297–326
Vesic A (1961) Bending of beams resting on isotropic elastic solid. J Eng Mech Div Proc ASCE 87(EM2):35–53
Yin JH (2000) Comparative modeling study of reinforced beam on elastic foundation. J Geotech Geoenviron Eng 126:265–271
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Basudhar, P.K., Yadav, S.K. & Basudhar, A. Treatise on Winkler Modulus of Subgrade Reaction and Its Estimation for Improved Soil–Structure Interaction Analysis. Geotech Geol Eng 36, 3091–3109 (2018). https://doi.org/10.1007/s10706-018-0523-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10706-018-0523-x