Experimental and empirical shear modulus reduction curves for a wide range of strains

Abstract

Understanding the shear modulus reduction behavior of soils under varying strain levels is vital for predicting soil response during seismic events. This study investigates the shear modulus reduction of diverse soil types using combined resonant column and cyclic triaxial tests. A single specimen is employed for both small and large strain ranges, which differs from conventional approaches that utilize two separate specimens. The shear modulus is assessed using different elastic moduli (E₁, E′₁, E₂, and E₃) within the stress-strain hysteresis loop, considering both compressional and extensional cyclic loadings. Results show significant deviation in secant moduli (G₁, G′₁, G₂, and G₃), varying from less than 20 % at small strains to 25–130 % at large strains, with hysteretic behavior becoming more asymmetrical at higher shear strains. Confining pressure (CP), relative density (RD), and coefficient of uniformity (C_U) are identified as critical factors influencing modulus reduction. A two-parameter model was developed to accurately capture the strain-dependent normalized shear modulus behavior. Parameter ‘a’ is found to be independent of RD, CP, and C_U, while reference strain ‘γ_ref’ shows a strong dependency on confining pressure with an indeterminate relationship with relative density. Poorly graded soils exhibit higher stiffness with greater ‘γ_ref’ values. The newly proposed mean, upper and lower bound curves can predict normalized shear modulus up to 10 % shear strains, significantly enhancing predictive capabilities beyond the typical 1 % strain limits of existing models. This improvement provides a more accurate basis for seismic response analysis, particularly in regions with similar soil types.