Development of a calibrated Pasternak foundation model for practical use Asrat Worku* A calibrated continuum foundation model of the order same as those of Pasternak, Filonenko-Borodich, and Vlasov is developed. This is achieved by seeking equality of the surface deformation of a Pasternak-type model with that of a calibrated Kerr-type model presented recently without neglecting any stress, strain, or deformation component in the continuum. In order to alleviate the sensitiveness of the model parameters to the layer thickness, this is eliminated from the corresponding expressions through the introduction of a dimensionless calibration parameter. The superiority of the new model over existing models of similar order has been demonstrated. Closed-form calibrated relationships for the two parameters of the new model are provided together with values of the calibration factor. The use of the model is illustrated on a basic problem of a beam on an elastic foundation. As a Pasternak-type model is more familiar to engineers and much easier to handle in applications than a Kerr-type model, its use in practice is recommended. The new model completes a series of calibrated models at three different levels: Winkler, Pasternak, and Kerr as proposed recently by the author. Keywords: Pasternak model, Kerr model, Foundation model parameters, Calibration, Continuum model, Mechanical model Introduction The introduction of multiple-parameter mechanical founda- tion models since 1950s has been an important development in foundation modeling. The main intention of these models was to improve on the inherent lack of shear interaction among the individual springs of the long-enduring model of Winkler (1867). To this effect, these models introduced additional mechanical elements of one type or another to interconnect the springs (Filonenko-Borodich, 1950; Hetenyi, 1950; Pasternak, 1954; Kerr, 1964). In a parallel development, attempts have also been made to devise continuum models. Most of these models are based on idealization of the foundation soil as a simplified continuum. Perhaps, the most pioneering work is that of Reissner (1958), who idealized the foundation soil as an elastic continuum of finite thickness overlying a rigid base and neglected the in-plane stress components on the elemental stress cube to simplify the associated mathematical work. Other simplified-continuum models have been introduced afterwards: Vlasov and Leont’ev (1966) neglected the horizontal deformation components and imposed an assumed mode of vertical deformation; Kerr and Rhines (1967) combined the assumptions of Reissner (1958) and Vlasov and Leont’ev (1966), less the imposition of a mode of vertical deformation, to obtain a mathematical model equivalent to that of Vlasov and Leont’ev (1966). 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. The sensitivity of the model parameters, particularly the spring coefficients, to the layer thickness was one of the major drawbacks that rendered such models less attractive to practicing engineers for a long time (Kerr, 1985; Worku, 2013). Civil Engineering Department, Addis Ababa University, P.O. Box 385, Addis Ababa, Ethiopia *Corresponding author, e-mail: asratie@gmail.com; aworku@gibbinternational. com Current address: Geotechnics, Gibb International, P.O. Box 30020, 00100 Nai- robi, Kenya. Fax: z254(0) 20 2210694/2244493; mobile: z251(0)725 617420 ß 2014 W. S. Maney & Son Ltd Received 7 October 2012; accepted 11 December 2012 26 DOI 10.1179/1938636213Z.00000000055 International Journal of Geotechnical Engineering 2014 VOL 8 NO 1