A Constitutive Model Controlling Damping for 2D and 3D Site Response

Modulus reduction and damping curves are commonly used as input parameters in site response analyses. Until very recently, constitutive models for nonlinear site response analysis could not accurately capture both the desired modulus reduction and damping behavior due to flaws in the assumed functional form for the backbone curve, and/or flaws in the unload-reload relationship. New relationships that solve these issues have recently been proposed, however, they are restricted to defining the in-plane stress-strain relationship for a single plane of shear, and are therefore only appropriate for 1D site response. This paper presents a multi-axial generalization of one of these 1D models, enabling its use in 2D and 3D site response. The 1D model is first briefly described, followed by the multi-axial generalization in terms of stress and strain invariants. The modulus reduction and damping curves are defined in terms of stress ratios rather than shear strains, which allows the model to better capture changes in confining pressure during undrained loading. An example is presented to illustrate fundamental differences in multiaxial versus 1D loading.