Abstract
Predictive equations for estimating normalized shear modulus and material damping ratio of sand are presented in this paper. The equations are based on a modified hyperbolic model and a statistical analysis of existing isotropically consolidated resonant column and strain-controlled cyclic direct simple shear test results for 252 specimens obtained from the Bay of Campeche. Two independent modified hyperbolic relationships are fitted to model stiffness (G/Gmax)-strain using two parameters and material damping ratio-strain curves using four parameters. Variables used in the equation for normalized shear modulus are: confining pressure; shear-strain amplitude; a reference strain, defined as the shear strain at which the shear modulus has reduced to 0.5Gmax, and a curvature parameter which controls the rate of modulus reduction, such as the model suggested by Darendeli (2001). The equation for damping ratio D, is expressed in terms of the reference strain, defined as the shear strain for a 50% increase in material damping ratio (i.e. D/Dmax = 0.5), a curvature parameter which controls the rate of material damping ratio increase, the minimum material damping ratio Dmin, and the maximum material damping ratio Dmax, similar to the equation suggested by Gonzalez and Romo (2011). It is found that the Bay of Campeche sand exhibit more linear response and lower damping ratio than other sands reported in the literature. The uncertainties associated with the predictive equations are quantified. A case study is provided to illustrate an application of the predictive equations to seismic response analysis and the importance of considering confining stress. The predictive equations of normalized shear modulus reduction G/Gmax and Damping ratio curves are easy to apply in practice, and are useful in the analysis of granular strata and offshore structures subjected to earthquake loading when site specific laboratory testing is not available.
