Simplified Model for Small-Strain Nonlinearity and Strength in 1D Seismic Site Response Analysis

Abstract

Commonly used simplified one-dimensional nonlinear seismic site response analyses employ constitutive models based on a variation of the hyperbolic model to represent the initial stress-strain backbone curve. Desirable features of the backbone curve include provision of (1) an initial shear modulus at zero shear strain, (2) a limiting shear stress at large shear strains, and (3) flexible control of the nonlinear behavior between those boundary conditions. Available hyperbolic models have combinations of two of these features. A new general quadratic/hyperbolic (GQ/H) model is developed from the bivariate quadratic equation to provide all desired features. Nonlinear behavior is controlled by a shear-strain-dependent curve-fitting function. The model’s unload-reload rules and coupling with pore-water pressure generation are also presented. Several total-stress site response analyses are presented to demonstrate the performance of the GQ/H model relative to a commonly used hyperbolic model in which the maximum shear stress cannot be defined. The analyses show the importance of properly representing the maximum shear stress in the constitutive model because it may lead to underestimation or overestimation of the computed site response.