Keywords: Preisach model, soil hysteresis, harmonic balance, site response.

Progress in the study of the cyclic behaviour of soils has led to the adoption of increasingly sophisticated and reliable mathematical representations. Hyperbolic, Ramberg-Osgood, Iwan-type, Masing models [1] are certainly the most currently available means for representing the cyclic behavior of soils subject to seismic loading. A persistent problem with the more widely used non-linear soil models employed in the site response analysis is their inability to match simultaneously the modulus reduction and damping curves [2]. To overcome this drawback in reference [3] an empirically based modified hyperbolic model altering the Masing rules has been developed. Gerolymos and Gazetas [4] proposed a phenomenological constitutive model based on the Bouc-Wen model. Recently, Philips and Hashash [2] proposed a hyperbolic model that modifies the Masing unloading-reloading rules.

The Preisach formalism [5] widely adopted in problems related to ferromagnetism, has recently received considerable attention in the study of the hysteretic behaviour of structural and mechanical systems. Site response is strongly affected by the nonlinear and hysteretic nature of the cyclic behaviour of soils. Thus, reliable hysteretic soil models have to be adopted in order to reliably assess the response of overlying structures. The most common approach for determining site response is based on the equivalent linear approach usually performed in the frequency domain. Although, this approach is computationally convenient it approximates the real nonlinear process of ground response through a set of linear analyses. Alternative approaches are based on the direct numerical integration of the equation of motion.

In this paper an alternative approach for modeling the cyclic behaviour of soils is proposed. The model is based on the Preisach formalism and it is defined to match simultaneously both modulus reduction and damping curves through a procedure of harmonic balance. Remarkably, closed form expressions of model parameters are suitably determined. The proposed hysteretic model was applied in a one-dimensional site response analysis in the time domain and it shows its efficiency for coping with wave propagation problems.

1

S.L. Kramer, "Geotechnical Earthquake Engineering", Englewood Cliffs, NJ, Prentice Hall, 1996.

2

C. Philips, Y.M.A. Hashash, "A simplified constitutive model to simultaneously match modulus reduction and damping soil curves for nonlinear site response analysis", Geothecnical Earthquake Engineering and Soil Dynamics IV, ASCE, (GSP 181) 1-10, 2008. doi:10.1061/40975(318)9

3

R.B. Darendeli, K.H. Stokoe, "Development of a new family of normalized modulus reduction and material damping curves", University of Texas at Austin, Austin, Geothecnical Engineering Report, GD01-1, 2001.

4

N. Gerolymos, G. Gazetas, "Constitutive model for 1-D cyclic soil behaviour applied to seismic analysis of layered deposits", Soils and Foundations, 45(3), 147-159, 2005.

5

F. Preisach, "Uber die magnetische nachwirkung", Zeitschrift fur Physik, 94, 277-302, 1935. doi:10.1007/BF01349418

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