A simplified constitutive model to simultaneously match modulus reduction and damping soil curves for nonlinear site response analysis

A persistent problem with the more widely used non-linear soil models employed in site response analysis is their inability to match measured modulus reduction and damping curves simultaneously. One possible approach for selecting a model's material properties is to match the modulus reduction curve obtained from soil tests while disregarding the mismatch with the damping curve. Although, this approach might work well when the soil is subjected to small strains, for large strains the damping is generally overestimated. Alternatively model parameters can be selected to approximately match both modulus reduction and damping curves over a desired strain range. Various authors proposed possible solutions to this mismatch. One approach uses a reduction factor for the hysteretic damping to better match the damping ratio at larger strains. Other approaches use advanced material constitutive models. This paper presents a new damping reduction factor, which modifies the hysteresis loops from the extended Masing rules, and a fitting procedure for both modulus reduction and damping curves. The damping reduction factor is implemented in conjunction with the hyperbolic model in the site response analysis program DEEPSOIL. Two examples of 1-D site response analyses are presented to illustrate the performance of the new formulation.