Part I: A Generalized Formulation of Continuum Models for Elastic Foundations

Development of a calibrated Pasternak foundation model for practical use

“…As mentioned in the Introduction, a generalized continuum subgrade model has recently been presented by Worku (2010) based on a physical model of an isotropic elastic layer of thickness H overlying a rigid half space. No stress, strain, or displacement component was neglected a priori unlike other models proposed in the past.…”

“…Without getting into the details, the mathematical relationship obtained between the vertical normal stress, p, and the surface deflection, w 0 , takes the following form of a partial differential equation of second order (Worku, 2010):…”

“…Recently, Worku (2010), based on a similar idealization of a layered continuum, but without neglecting any stress, deformation, or strain components, presented a continuum model of the order same as that of Reissner, yet with significant improvements in the coefficients. He showed that this new model is a generalization of the existing continuum models that reduces to the level of Reissner's (1958) model when the horizontal stress components in the continuum are dropped; to the level of Kerr and Rhines (1967) or Vlasov and Leont'ev (1966) if the horizontal deformation components alone are neglected; and to a Winkler-type simplified-continuum model when the vertical shear stress components are neglected.…”

“…More recently, Worku (2013) synthesized his rigorous model (Worku, 2010) with the equivalent three-parameter mechanical model of Kerr (1964) and suggested calibrated formulae for Kerr's model parameters in terms of the continuum parameters. In doing so, he eliminated the thickness of the elastic continuum from the expressions of the model parameters, which are sensitive to this quantity.…”

“…Despite the development of numerous commercial finite-element (FE) software, renewed interest in this topic of analytical foundation modeling is on the rise recently (Avramidis and Morfidis, 2006;Colasanti and Horvath, 2010;Failla et al, 2013;Horvath and Colasanti, 2011;Tanahashi, 2004;Wang et al, 2005;Worku, 2010;Worku and Degu, 2010;Worku, 2013;Yin, 2000). This could be attributed to a number of reasons including the mesh dependence of FE modeling, lack of accurate geotechnical data for use in advanced constitutive relationships, relative difficulty to use FE models to solve routine problems in design offices like modeling the soil and structure together as a unit, and need for controlling FE analysis results.…”