Confining Stress-Dependencies of Shear Modulus Reduction and Damping Models for Sands

Abstract

Normalized shear modulus reduction (G/Gmax) models represent the nonlinear shear stress-shear strain response of soils. Modulus Reduction and Damping (MRD) curves are used to obtain degraded soil properties for equivalent-linear site-response analysis, calibrate nonlinear stress–strain models, and examine the influence of effective confining stress on stress response tied to liquefaction triggering. These curves are affected by mean effective confining stress. Published models represent this confining stress effects using different equations and parameters, which makes the direct comparison across models difficult. This thesis develops and evaluates a unified framework that separates the normalized shear modulus reduction into a strain-dependent function, K(γ), and a strain-dependent confining stress exponent, Δm(γ). Four published models, Ishibashi and Zhang (1993), Darendeli (2001), Wang and Stokoe (2022), and the GQ/H model of Groholski et al. (2016) were evaluated. A clean sand condition is used so that the differences in the results were mainly related to differences among the models. At each shear strain, K(γ) is defined from the original model response at 1 atm, while Δm(γ) is then fitted over the remaining confining stress levels in linear G/Gmax space. A continuous strain-dependent function of Δm(γ) is then developed to reconstruct each model within the generalized framework. The original and generalized models are compared through normalized modulus-reduction curves, derived shear stress backbones, theoretical Masing-damping curves and shear stress normalized by mean effective confining stress. The generalized forms reproduce the responses of the original models closely over the evaluated ranges. The fitted stress exponents are also related directly to the confining stress and curvature parameters of the original models, which help explain the differences among their stress-dependent response. The normalized shear stress ratios provide a basis for extending the framework to investigate the effect of confining stress on liquefaction triggering. The proposed framework provides a method for comparing different models and examining how their modulus reduction behavior affects the corresponding shear stress and theoretical damping responses. Future work should evaluate the framework using laboratory measurements from the same sand tested at several confining stresses.